WO2018137568A1 - 编码方法、编码装置和通信装置 - Google Patents

编码方法、编码装置和通信装置 Download PDF

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Publication number
WO2018137568A1
WO2018137568A1 PCT/CN2018/073435 CN2018073435W WO2018137568A1 WO 2018137568 A1 WO2018137568 A1 WO 2018137568A1 CN 2018073435 W CN2018073435 W CN 2018073435W WO 2018137568 A1 WO2018137568 A1 WO 2018137568A1
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Prior art keywords
sequence
bits
code length
channel numbers
polarization channel
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PCT/CN2018/073435
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English (en)
French (fr)
Inventor
陈莹
张公正
张华滋
罗禾佳
李榕
王俊
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华为技术有限公司
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Priority to EP18744523.4A priority Critical patent/EP3553982A4/en
Publication of WO2018137568A1 publication Critical patent/WO2018137568A1/zh
Priority to US16/523,954 priority patent/US10673654B2/en

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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0204—Channel estimation of multiple channels
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/63—Joint error correction and other techniques
    • H03M13/635—Error control coding in combination with rate matching
    • H03M13/6362—Error control coding in combination with rate matching by puncturing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0041—Arrangements at the transmitter end
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03178—Arrangements involving sequence estimation techniques
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0041—Arrangements at the transmitter end
    • H04L1/0043—Realisations of complexity reduction techniques, e.g. use of look-up tables

Definitions

  • Embodiments of the present invention relate to the field of communications, and more particularly, to an encoding method, an encoding apparatus, and a communication apparatus.
  • Polar codes proposed by Turkish professor Arikan are the first good code to theoretically prove that Shannon capacity can be achieved with low coding complexity.
  • the Polar code is a linear block code whose coding matrix is G N , for example, the encoding process is among them Is a binary line vector with a length of N (ie, the length of the mother code); G N is an N ⁇ N matrix, and Defined as the Kronecker product of log 2 N matrices F 2 .
  • GN.(A) is a submatrix obtained from those rows corresponding to the index in the set A in GN.
  • GN(AC) is a submatrix obtained in the GN by those rows corresponding to the indexes in the set AC.
  • the construction process of the Polar code is a collection
  • the selection process determines the performance of the Polar code.
  • the construction process of the Polar code is generally: determining that there are N polarized channels in total according to the length N of the mother code, respectively corresponding to N rows of the coding matrix, calculating the reliability of the polarized channel, and the first K polarizations with higher reliability.
  • the index of the channel is the element of set A, and the index corresponding to the remaining (NK) polarized channels is used as the index set of fixed bits.
  • Set A determines the position of the information bits, the set The position of the fixed bit is determined.
  • the original Polar code (parent code) has a code length of 2, which is generally required to achieve a Polar code of arbitrary code length by rate matching.
  • puncture or puncture can be used. Rate matching is achieved in a shortened manner.
  • polarization channel reliability includes error probability, channel capacity and polarization weight.
  • there are three methods for estimating the reliability of a polarized channel and one is to calculate the Babbitt of each polarized channel (Bhattacharyya). a parameter that reflects the error probability of the polarized channel and then selects the polarization channel placement information bits corresponding to the K smallest Pap's parameters, but the method is only applicable to the binary erasure channel, and cannot be accurately performed for other channels.
  • the reliability is estimated, so the performance is not high; the other two are Density evolution (DE) method and Gaussian approximation (GA).
  • DE Density evolution
  • GA Gaussian approximation
  • the DE method and the GA method depend on the parameter rate matching method of the actual channel, the code rate and the modulation method when calculating the reliability.
  • the reliability estimation result of the changed polarization channel of any one of the above parameters also changes, and the position of the corresponding information bit also changes, which eventually leads to excessive storage overhead.
  • the embodiments of the present application provide an encoding method, an encoding device, and a communication device, which can reduce the storage complexity of the Polar code encoding and improve the performance of the Polar code.
  • an encoding method comprising:
  • N a positive integer
  • the determining the N to be coded bits includes:
  • the acquiring the first sequence that includes the N polarization channel numbers includes:
  • a first sequence comprising N polarized channel sequences is obtained from the sequence in Table 1 of the Appendix or the equivalent replacement sequence of the sequence in Table 1.
  • the determining the N to be coded bits includes:
  • N N according to M, where symbol Indicates rounding down, the M is the target code length of the Polar code output, the M is not equal to the positive power of 2, and M is a positive integer.
  • the N to-be-coded bits correspond to a mother code whose code length is N
  • the obtaining the first sequence including the N polarization channel numbers includes:
  • the first sequence of the communication system supports a maximum of the first sequence S max maximum base code length N max corresponds to a first determined sequence of the mother code corresponding to the code length N, wherein the mother code corresponding to the code length N
  • the maximum first sequence S max is an equivalent replacement of the sequence in the Appendix Table 1 or the sequence in Table 1
  • the N bits to be encoded correspond to N coded bits
  • the obtaining the first sequence including the N polarization channel numbers includes:
  • the N to-be-coded bits correspond to a mother code whose code length is N
  • the obtaining the first sequence including the N polarization channel numbers includes:
  • the first sequence corresponding to N is the first sequence including the N polarization channel numbers.
  • the fourth sequence is an equivalent replacement sequence of the sequence in Table 1 or the sequence in Table 1 in the Appendix.
  • the N bits to be encoded correspond to N coded bits
  • Determining, according to the fourth sequence corresponding to the code length of the mother code N, that the rate code N is not required to perform the rate matching, the first sequence corresponding to the code length N of the mother code includes:
  • the acquiring the first sequence that includes the N polarization channel numbers includes:
  • a first sequence comprising N polarized channel sequences is obtained from the sequence in Table 2, Table 3 or Table 4 of the Appendix or the equivalent replacement sequence of the sequence in Table 2, Table 3 or Table 4.
  • the acquiring the first sequence that includes the N polarization channel numbers includes:
  • a second sequence of N S 1, S 2, ..., S N is determined first sequence S 'N, a second sequence comprising i i S polarizations channel number, 1 ⁇ i ⁇ N, i is a positive integer.
  • the determining the first sequence according to the N second sequences S 1 , S 2 , . . . , S N S' N includes:
  • the first sequence S' N is calculated based on the following formula:
  • an encoding apparatus including:
  • a determining module configured to determine N bits to be encoded, where N is a positive integer
  • An obtaining module configured to acquire a first sequence that includes N polarized channel numbers
  • the determining module is further configured to determine, according to the first sequence, a location of information bits in the N to-be-coded bits;
  • the encoding module is configured to perform Polar coding on the N to-be-coded bits to obtain coded bits.
  • the determining module is specifically configured to:
  • the acquiring module is specifically configured to:
  • a first sequence comprising N polarized channel sequences is obtained from the sequence in Table 1 of the Appendix or the equivalent replacement sequence of the sequence in Table 1.
  • the determining module is specifically configured to:
  • N N according to M, where symbol Indicates rounding down, the M is the target code length of the Polar code output, the M is not equal to the positive power of 2, and M is a positive integer.
  • the N to-be-coded bits correspond to a mother code whose code length is N
  • the obtaining module is specifically configured to:
  • the first sequence of the communication system supports a maximum of the first sequence S max maximum base code length N max corresponds to a first determined sequence of the mother code corresponding to the code length N, wherein the mother code corresponding to the code length N
  • the maximum first sequence S max is an equivalent replacement of the sequence in the Appendix Table 1 or the sequence in Table 1
  • the N bits to be encoded correspond to N coded bits
  • the obtaining module is specifically configured to:
  • the N to-be-coded bits correspond to a mother code whose code length is N
  • the obtaining module is specifically configured to:
  • the first sequence corresponding to N is the first sequence including the N polarization channel numbers.
  • the fourth sequence is an equivalent replacement sequence of the sequence in Table 1 or the sequence in Table 1 in the Appendix.
  • the N bits to be encoded correspond to N coded bits
  • the obtaining module is specifically configured to:
  • the acquiring module is specifically configured to:
  • a first sequence comprising N polarized channel sequences is obtained from the sequence in Table 2, Table 3 or Table 4 of the Appendix or the equivalent replacement sequence of the sequence in Table 2, Table 3 or Table 4.
  • the acquiring module is specifically configured to:
  • a second sequence of N S 1, S 2, ..., S N is determined first sequence S 'N, a second sequence comprising i i S polarizations channel number, 1 ⁇ i ⁇ N, i is a positive integer.
  • the acquiring module is specifically configured to:
  • the first sequence S' N is calculated based on the following formula:
  • a communication device including:
  • a processor configured to execute the program stored in the memory, when the program is executed, the processor is configured to perform any one of the foregoing first aspect or the first aspect.
  • Yet another aspect of the present application is directed to a computer readable storage medium having instructions stored therein that, when executed on a computer, cause the computer to perform the methods described in the various aspects above.
  • Yet another aspect of the present application provides a computer program product comprising instructions which, when run on a computer, cause the computer to perform the methods described in the various aspects above.
  • Yet another aspect of the present application provides a computer program that, when run on a computer, causes the computer to perform the methods described in the various aspects above.
  • determining the location of the information bits in the to-be-coded bits based on the obtained first sequence including the N polarization channel numbers may improve the performance of the Polar code.
  • 2a is a schematic diagram of a basic flow of a wireless communication transmitting end and a receiving end;
  • 2b is a schematic diagram of a coding process of a Polar code implemented in the present application.
  • 3a is a schematic flow chart of an encoding method implemented by the present application.
  • Figure 3b is a flow chart of still another embodiment of step 302 of Figure 3a;
  • Figure 3c is a flow chart of still another embodiment of step 302 of Figure 3a;
  • Figure 3d is a flow chart of still another embodiment of step 302 of Figure 3a;
  • 4a is a schematic flow chart of another coding method implemented by the present application.
  • Figure 4b is a flow chart of still another embodiment of step 402 of Figure 4a;
  • FIG. 5 is a structural diagram of an encoding apparatus implemented in the present application.
  • FIG. 6 is a structural diagram of a communication device implemented by the present application.
  • GSM Global System of Mobile communication
  • CDMA Code Division Multiple Access
  • WCDMA Wideband Code Division Multiple Access
  • GPRS General Packet Radio Service
  • LTE Long Term Evolution
  • FDD Frequency Division Duplex
  • TDD Time Division Duplex
  • UMTS Universal Mobile Telecommunication System
  • a component can be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, and/or a computer.
  • an application running on a computing device and a computing device can be a component.
  • One or more components can reside within a process and/or execution thread, and the components can be located on one computer and/or distributed between two or more computers.
  • these components can execute from various computer readable media having various data structures stored thereon.
  • a component may, for example, be based on signals having one or more data packets (eg, data from two components interacting with another component between the local system, the distributed system, and/or the network, such as the Internet interacting with other systems) Communicate through local and/or remote processes.
  • data packets eg, data from two components interacting with another component between the local system, the distributed system, and/or the network, such as the Internet interacting with other systems
  • An access terminal may also be called a system, a subscriber unit, a subscriber station, a mobile station, a mobile station, a remote station, a remote terminal, a mobile device, a user terminal, a terminal, a wireless communication device, a user agent, a user device, or a UE (User Equipment, User equipment).
  • the access terminal may be a cellular phone, a cordless phone, a SIP (Session Initiation Protocol) phone, a WLL (Wireless Local Loop) station, a PDA (Personal Digital Assistant), and a wireless communication.
  • the base station can be used for communication with a mobile device, and the base station can be a BTS (Base Transceiver Station) in GSM (Global System of Mobile communication) or CDMA (Code Division Multiple Access), or
  • the NB (NodeB, base station) in the WCDMA (Wideband Code Division Multiple Access) may be an eNB or an eNodeB (Evolved Node B) in LTE (Long Term Evolution).
  • System 100 includes a base station 102 that can include multiple antenna groups.
  • one antenna group may include antennas 104 and 106
  • another antenna group may include antennas 108 and 110
  • additional groups may include antennas 112 and 114.
  • Two antennas are shown for each antenna group, however more or fewer antennas may be used for each group.
  • Base station 102 can additionally include a transmitter chain and a receiver chain, as will be understood by those of ordinary skill in the art, which can include multiple components associated with signal transmission and reception (e.g., processor, modulator, multiplexer, demodulation) , demultiplexer or antenna, etc.).
  • Base station 102 can communicate with one or more access terminals, such as access terminal 116 and access terminal 122. However, it will be appreciated that base station 102 can communicate with substantially any number of access terminals similar to access terminals 116 and 122. Access terminals 116 and 122 can be, for example, cellular telephones, smart phones, portable computers, handheld communication devices, handheld computing devices, satellite radios, global positioning systems, PDAs, and/or any other for communicating over wireless communication system 100. Suitable for equipment. As shown, access terminal 116 is in communication with antennas 112 and 114, with antennas 112 and 114 transmitting information to access terminal 116 over forward link 118 and receiving information from access terminal 116 over reverse link 120.
  • access terminal 116 is in communication with antennas 112 and 114, with antennas 112 and 114 transmitting information to access terminal 116 over forward link 118 and receiving information from access terminal 116 over reverse link 120.
  • access terminal 122 is in communication with antennas 104 and 106, wherein antennas 104 and 106 transmit information to access terminal 122 over forward link 124 and receive information from access terminal 122 over reverse link 126.
  • FDD Frequency Division Duplex
  • the forward link 118 can utilize a different frequency band than that used by the reverse link 120, and the forward link 124 can utilize the reverse link 126. Different frequency bands used.
  • the forward link 118 and the reverse link 120 can use a common frequency band, and the forward link 124 and the reverse link 126 can use a common frequency band.
  • Each set of antennas and/or regions designed for communication is referred to as a sector of base station 102.
  • the antenna group can be designed to communicate with access terminals in sectors of the coverage area of base station 102.
  • the transmit antennas of base station 102 may utilize beamforming to improve the signal to noise ratio for forward links 118 and 124 of access terminals 116 and 122.
  • the base station 102 transmits to the randomly dispersed access terminals 116 and 122 in the relevant coverage area by the base station as compared to all of the access terminals transmitted by the base station, the mobile devices in the adjacent cells are subject to Less interference.
  • base station 102, access terminal 116, and/or access terminal 122 may be transmitting wireless communication devices and/or receiving wireless communication devices.
  • the transmitting wireless communication device can encode the data for transmission.
  • the transmitting wireless communication device can have (eg, generate, obtain, store in memory, etc.) a certain number of information bits to be transmitted over the channel to the receiving wireless communication device.
  • Such information bits may be included in a transport block (or multiple transport blocks) of data that may be segmented to produce a plurality of code blocks.
  • the transmitting wireless communication device can encode each code block using a Polar code encoder (not shown).
  • 2a is a basic flow of wireless communication.
  • the source is sequentially transmitted after source coding, channel coding, and digital modulation.
  • the destination is outputted by digital demodulation, channel decoding, and source decoding.
  • the channel codec can use a Polar code. Since the code length of the original Polar code (parent code) is an integer power of 2, in practical applications, a Polar code of arbitrary code length needs to be implemented by rate matching. As shown in FIG. 2a, rate matching is performed after channel coding at the transmitting end to implement an arbitrary target code length, and at the receiving end, de-rate matching is performed before channel decoding.
  • the encoding process of the Polar code includes three processes of construction, coding, and rate matching.
  • the first is a construction process: receiving the input N1 information bits, and determining a sequence corresponding to the mother code length N according to the mother code length N, wherein the mother code length N is determined according to the encoded target code length M, to be encoded.
  • the number of bits is N
  • the N bits to be encoded include N1 information bits and N2 fixed bits, and the position of the information bits is determined from the sequence according to the number of information bits, that is, the position of the fixed bits is determined;
  • Encoding process Polar encoding the bit to be encoded to obtain the bit encoded by Polar;
  • the rate matching process since the code length of the encoded code of the Polar code (ie, the code length of the mother code) is a positive integer power of 2, the practical application In general, it is necessary to implement a Polar code of arbitrary code length by rate matching.
  • a rate matching can be implemented by using a puncture or a shortening scheme.
  • the specific implementation is to delete a part of the code length of a positive integer power of 2.
  • NM bits the target code length is obtained, where N, M, N1, and N2 are all positive integers.
  • the coding method provided by the embodiment of the present invention relates to the Polar code coding process shown in FIG. 2b, and most relates to a construction process, that is, how to determine the position of information bits.
  • An embodiment of the present invention provides an encoding method, which determines the location of information bits in a to-be-coded bit based on the obtained first sequence of N polarization channel numbers, which can improve the performance of the Polar code.
  • the target code length of the Polar code output can be a positive power of 2 or a positive integer power of 2, the target of the Polar code output.
  • the code length is a positive integer power of 2
  • no rate matching is required
  • the target code length of the Polar code output is not a positive integer power of 2
  • rate matching is required.
  • Figure 3a depicts an encoding method flow 300, which is described in detail below in conjunction with Figure 3a.
  • N M
  • M the positive integer power of the target code length of the Polar code output equal to 2
  • M is a positive integer
  • the N bits to be coded correspond to N polarized channels, and one bit corresponds to one polarized channel.
  • Appendix Table 1 gives the first sequence that N corresponds to when taking different values.
  • N is the bit length to be encoded
  • the elements in each first sequence in the table are the sequence numbers of the polarized channels. All or part of the first sequence of Table 1 may be stored in the communication system to which the present embodiment is applied.
  • Tables 2 and 3 and Table 4 referred to in Table 1 and subsequent embodiments are merely examples, and Tables 1, 2, 3, and 4 are not affected by the overall effect.
  • the sequence in the following can be adjusted to include, but is not limited to, the following aspects:
  • Each of the first sequences in Table 1, Table 2, Table 3, and Table 4 contains N elements starting from 1 to ending N, where N is the mother code length, and N elements ending from 1 to N represent N.
  • the serial number of the polarized channel In fact, the sequence numbers of the N polarized channels can also start from 0 to the end of N-1. Therefore, subtract 1 from each element in the first sequence in Table 1, Table 2, Table 3, and Table 4 in the current Appendix. N elements including starting from 0 to ending N-1 can be formed.
  • the sequence number or identifier of the above polarized channel may also be represented in other ways, and the specific expression does not affect the specific location of the polarized channel represented in the table.
  • the position of the polarization channel corresponding to the first K or the last K polarization channel numbers is taken as the position of the information bit, and the other polarization channel positions are used as the positions of the fixed bits, thereby obtaining the information bits.
  • the position of the fixed bit where K is the number of information bits in the N bits to be encoded, and K is a positive integer less than N.
  • the embodiment does not limit the position of the polarization channel corresponding to the first K or the last K polarization channel numbers in the first sequence as the information bits.
  • the position of the information bit determined by the first sequence satisfies the inclusion relationship, that is, the set of K information bit positions is determined to be a subset of the set of K+m information bit positions, where m is a positive integer, thereby lowering Polar
  • the set of K information bit positions is determined to be a subset of the set of K+m information bit positions, where m is a positive integer, thereby lowering Polar
  • the encoding process of the bit to be encoded may be completed by using the encoding matrix F N of the Polar code, thereby obtaining the encoded code of the Polar encoding.
  • the above embodiment mainly differs in step S302, so that the computational complexity of constructing the first sequence is greatly reduced by storing the first sequence S in the communication system.
  • a first embodiment according to a sequence of S302 in the embodiment may be 1, S 2, ..., S N to generate a first sequence S 'N N
  • the second sequence S The second sequence S i includes the sequence numbers of the i polarization channels, that is, includes i elements, and the second sequence S i is determined based on the reliability of the N polarization channels, 1 ⁇ i ⁇ N, and i is a positive integer.
  • S302a The second sequence of N S 1, S 2, ..., S N to generate a first sequence S 'N comprises:
  • a second sequence S i Determining, according to the reliability of the N polarized channels, a second sequence S i , where the second sequence S i includes i polarized channel numbers, and the i polarized channel numbers correspond to i polarized channels, where i
  • the reliability of any of the polarized channels is greater than the reliability of the (Ni) polarized channels of the N polarized channels except the i polarized channels.
  • the i elements (ie, i polarization channel numbers) included in the second sequence S i may be sorted according to the reliability of the polarization channel, or may not be sorted according to the reliability of the polarization channel. That is, it can be a collection that is not sorted.
  • the reliability of the N polarized channels is determined, and the sequence of the polarization channel corresponding to the maximum reliability among the determined reliability of the N polarized channels is used as the second sequence S 1, S 1, i.e. comprising a number corresponding to the maximum reliability polarization channels, and since the S 1 contains one element, and therefore, the element contained in S 1 ordering concept does not exist.
  • the reliability of common polarization channels is measured by error probability, channel capacity, polarization weight, etc.
  • a Gaussian approximation algorithm or a density evolution algorithm can be utilized to determine the reliability of a polarized channel.
  • the present invention does not limit the algorithm used to determine the reliability of a polarized channel.
  • the first sequence S' i is calculated using the following formula:
  • ⁇ represents the difference set of the two sequences is calculated, for example, the sequence [1 2 3] ⁇ [1 3 2 4] is [4], and the "+" indicates that the two will be before and after The sequences are joined to form a sequence, for example, [3 2 1] + [4] is [3 2 1 4].
  • step S301a, S303a, and S304a may refer to the foregoing S301, S303, and S304, respectively, and details are not described herein again.
  • this embodiment mainly differs in step S302a, so that the storage system greatly saves storage resources by not storing the first sequence.
  • the first sequence S corresponding to the current mother code length N may be determined according to the maximum first sequence S max corresponding to the maximum mother code length N max supported by the communication system.
  • the maximum first sequence S max may be protocol-defined and stored in the communication system.
  • the maximum first sequence S max may be that N in Table 1 in Embodiment 1 is between 256 and 1024, or 1024 and 2048.
  • the first sequence corresponding to the time interval may also be the first sequence generated and stored according to the generation method in the second embodiment.
  • the maximum mother code size of Polar code of the current Polar code can be:
  • the embodiment includes:
  • S301b Determine N bits to be encoded.
  • N ⁇ N max and M is a non-maximum target code length of the Polar code that is not equal to a positive integer power of 2, and M is a positive integer.
  • the N to-be-coded bits correspond to the current mother code whose code length is N
  • N is the current mother code code length is less than the maximum mother code code length N
  • the current mother code code length N needs to undergo rate matching to obtain the target code length M.
  • S302b Acquire a first sequence that includes N polarization channel numbers.
  • the first sequence corresponding to the current mother code length N is determined according to the maximum first sequence S max corresponding to the maximum mother code length N max supported by the communication system, and specifically includes:
  • the maximum sequence S max, S max maximum first sequence may be agreed upon, and stored in the communication system, e.g., the first sequence S max Maximum embodiment may be a The first sequence in which the N in Table 1 is between 256 and 1024, or between 1024 and 2048, may also be the first sequence generated and stored according to the generation method in Embodiment 2.
  • S302b2 determining a location of N-M bits to be deleted in the N codes, where N coded bits correspond to N coded bits;
  • the rate matching can be achieved by using the short position in the punch mode or the short position in the short mode, and therefore, the NM bits to be deleted are
  • the position may be a punching position in the punching mode or a shorting position in the short mode, wherein the punching mode may be a reverse order from the heading to the back or from the heading, and the short mode may be from the back to the front or from the back. The previous bit is reversed.
  • the position of the preceding NM bits is set to 0, and the position of other bits is set to 1, ie Among them, “0” indicates the punching position, and “1” indicates the unpunched position.
  • the bit reverse order is performed on the punching position from the heading.
  • the bit reverse order is to convert a decimal integer into a binary form, reverse the order of the binary elements, and convert the inverted binary number into decimal, and the newly obtained number is The bit reverse order value of the original number.
  • the auxiliary sequence of length N is initialized (ie, from the punched position after going to the left), the first NM elements are set to 0, the last M elements are 1, N represents the mother code length, and M represents the target code length, wherein Where "0" indicates the punch position and "1" indicates the unpunched position.
  • the auxiliary sequence is:
  • the auxiliary sequence Perform bit reverse order rearrangement to obtain punch mode That is, the bit reverse order punching mode from the heading, wherein
  • D(b 1 b 2 ... b n ) converts the binary sequence b 1 b 2 ... b n into a decimal number
  • NM bits The position of the following NM bits is set to 0, and the position of other bits is set to 1, ie Where "0" indicates the short position and "1" indicates the non-shorten position.
  • the bit reverse order is performed on the short position from the back to the front.
  • the auxiliary sequence of length N is initialized, and the first M elements are set to 1, the last N-M elements are 0, N represents the mother code length, and M represents the target code length, and the auxiliary sequence is:
  • D(b 1 b 2 ... b n ) converts the binary sequence b 1 b 2 ... b n into a decimal number
  • S303b Determine, according to the first sequence, a location of information bits in the N to-be-coded bits.
  • the position of the polarization channel corresponding to the first K or the last K polarization channel numbers in the first sequence may be taken as the position of the information bit, and the other polarization channel positions are the positions of the fixed bits, where K is N The number of information bits in the bits to be encoded.
  • S304b Perform Polar coding on the N to-be-coded bits to obtain coded bits.
  • this embodiment differs from other embodiments mainly in step S302b, such that only the largest first sequence S max needs to be stored in the communication system , thereby saving storage space and, in addition, the first sequence
  • the computational complexity of the construction process is also relatively low.
  • the first sequence corresponding to the same mother code length N when rate matching is required may be determined according to the fourth sequence corresponding to the mother code length N without performing rate matching.
  • the fourth sequence corresponding to the length of the mother code code length N may be protocol-defined and stored in the communication system.
  • the fourth sequence may be in the first embodiment.
  • the first sequence corresponding to the time may also be the first sequence generated and stored according to the generating method in the second embodiment.
  • the mother code length N will be described as follows to determine the corresponding first sequence when rate matching is required. As shown in Figure 3d, this embodiment includes:
  • S301c Determine N bits to be encoded.
  • M is the positive integer power of the Polar code whose target code length is not equal to 2, and M is a positive integer.
  • the N to-be-coded bits correspond to the mother code whose code length is N, and the mother code length N needs to be rate matched to obtain the target code length M.
  • the first sequence corresponding to the code length N of the mother code is determined according to the fourth sequence corresponding to the code length N of the mother code, including:
  • S302c1 Obtain a fourth sequence corresponding to the mother code length N when no rate matching is needed.
  • the fourth sequence corresponding to the mother code length N without rate matching may be protocol-stipulated and stored in the communication system.
  • the fourth sequence may be in the first embodiment.
  • the first sequence corresponding to the different values may also be the first sequence generated and stored according to the generating method in the second embodiment.
  • S302c2 Determine a position of the N-M bits to be deleted among the N coded bits, where the N bits to be coded correspond to N coded bits.
  • the mother code length N needs to be rate matched to obtain the target code length M, it is usually possible to achieve rate matching by using the short position in the punch mode or the short position in the short mode, and therefore, the position of the NM bits to be deleted. It may be the punch position in the punch mode or the short position in the short mode.
  • the punch position or the short position refer to the related description above.
  • S303c Determine, according to the first sequence, a location of information bits in the N to-be-coded bits.
  • the position of the polarization channel corresponding to the first K or the last K polarization channel numbers in the third sequence may be taken as the position of the information bit, and the other polarization channel positions are the positions of the fixed bits, where K is N The number of information bits in the bits to be encoded.
  • the embodiment does not limit the position of the polarization channel corresponding to the first K or the last K polarization channel numbers in the first sequence as the information bits.
  • S304c Perform Polar coding on the N to-be-coded bits to obtain coded bits.
  • the encoding process of the bit to be encoded may be completed by using the encoding matrix F N of the Polar code, thereby obtaining the encoded code of the Polar encoding.
  • the embodiment differs from the other embodiments mainly in step S302c, such that only the fourth sequence corresponding to the mother code length N is required to be used for rate matching is stored in the communication system, thereby The storage space is saved.
  • the computational complexity of the first sequence of the mother code length N corresponding to the rate matching needs to be relatively low.
  • the first sequence corresponding to the mother code length N when rate matching is required is determined according to the table in the related appendix.
  • FIG. 4a illustrates a coding method flow 400 provided by another embodiment of the present invention.
  • the coding process includes:
  • the mother code length N needs to be rate matched to obtain the target code length M.
  • Appendix Table 2 gives the first sequence for which M and N correspond to different values.
  • M is the target code length of the Polar code
  • N is the number of bits to be encoded
  • the elements in each first sequence are polarization channel numbers.
  • Appendix Table 3 gives the first sequence corresponding to when M and N take different values.
  • M is the target code length of the Polar code
  • N is the number of bits to be encoded
  • the elements in each first sequence are polarization channel numbers.
  • Appendix Table 4 gives the first sequence corresponding to M and N when taking different values.
  • M is the target code length of the Polar code
  • N is the number of bits to be encoded
  • the elements in each first sequence are polarization channel numbers.
  • S403. Determine, according to the first sequence, a location of information bits in the N to-be-coded bits.
  • the position of the polarized channel corresponding to the first K polarized channel numbers is taken as the position of the information bits, and the other polarized channel positions are used as the positions of the fixed bits, thereby obtaining information bits and fixed bits.
  • the embodiment does not limit the position of the polarization channel corresponding to the first K or the last K polarization channel numbers in the first sequence as the information bits.
  • the encoding process of the bit to be encoded may be completed by using the encoding matrix F N of the Polar code, thereby obtaining the encoded code of the Polar encoding.
  • the mother code length N is determined according to the N second sequences S 1 , S 2 , . . . , S N corresponding to the need for rate matching.
  • the first sequence is determined according to the N second sequences S 1 , S 2 , . . . , S N corresponding to the need for rate matching.
  • the first sequence may be determined according to the N second sequences S 1 , S 2 , . . . , S N , where the second sequence S i includes the sequence numbers of the i polarized channels, that is, includes i Element, and the second sequence S i is determined based on the reliability of the N polarized channels, 1 ⁇ i ⁇ N, i is a positive integer.
  • S402a determining the first sequence according to the N second sequences S 1 , S 2 , . . . , S N includes:
  • N second sequences S 1 , S 2 , . . . , S N are determined .
  • a second sequence S i Determining, according to the reliability of the N polarized channels, a second sequence S i , where the second sequence S i includes i polarized channel numbers, and the i polarized channel numbers correspond to i polarized channels, where i
  • the reliability of any of the polarized channels is greater than the reliability of the (Ni) polarized channels of the N polarized channels except the i polarized channels.
  • the i elements (ie, i polarization channel numbers) included in the second sequence S i may be sorted according to the reliability of the polarization channel, or may not be sorted according to the reliability of the polarization channel. That is, it can be a collection that is not sorted.
  • the reliability of the N polarized channels is determined, and the sequence of the polarization channel corresponding to the maximum reliability among the determined reliability of the N polarized channels is used as the second sequence S 1, S 1, i.e. comprising a number corresponding to the maximum reliability polarization channels, and since the S 1 contains one element, and therefore, the element contained in S 1 ordering concept does not exist.
  • the reliability of common polarization channels is measured by error probability, channel capacity, polarization weight, etc.
  • a Gaussian approximation algorithm or a density evolution algorithm can be utilized to determine the reliability of a polarized channel.
  • the present invention does not limit the algorithm used to determine the reliability of a polarized channel.
  • Rate matching can usually be achieved by using a puncturing mode or a shortening mode.
  • the puncturing mode the puncturing position can be reversed from the time of going to or from the back.
  • the short mode the short position can be from the back to the front.
  • different punch positions or short positions may result in different reliability of the determined polarized channels, thereby generating different second sequences S i , for example, in the Gaussian approximation algorithm, different
  • the punch position or the short position affects the initialization value, which in turn calculates different error probabilities. Further description of how to use the punch position or the short position to calculate the error probability in the Gaussian approximation algorithm is further described.
  • the first sequence S' i is calculated based on the following formula:
  • ⁇ represents the difference set of the two sequences is calculated, for example, the sequence [1 2 3] ⁇ [1 3 2 4] is [4], and the "+" indicates that the two will be before and after The sequences are joined to form a sequence, for example, [3 2 1] + [4] is [3 2 1 4].
  • the other steps S401a, S403a, and S404a may refer to the foregoing S401, S403, and S404, respectively, and details are not described herein again.
  • the above embodiment mainly differs in step S402a, so that the storage system can greatly save storage resources by not storing the first sequence S.
  • the corresponding log likelihood ratio is initialized, and the log likelihood ratio mean value initial value of each code symbol position is obtained.
  • the log likelihood ratio mean value of each code symbol position is calculated using the following formula.
  • the log likelihood ratio average value indicating the position of the i-th code symbol is used, and ⁇ is used to indicate the noise of the signal.
  • the logarithm likelihood ratio mean value of each code symbol position is calculated using the following formula:
  • puncturingx(i) indicates that the i-th code symbol position is the punch position
  • Nopuncturingx(i) indicates that the i-th code symbol position is the non-punch position.
  • x(i) represents the i-th code symbol position, Indicates the log likelihood ratio mean value of the i-th code symbol position, and ⁇ is used to indicate the standard deviation of the signal noise.
  • the log-likelihood ratio mean value of each code symbol position is calculated using the following formula:
  • shortingx(i) indicates that the i-th code symbol position is a short position
  • NoShortingx(i) indicates that the i-th code symbol position is a non-shorten position.
  • the log-likelihood ratio mean is recursively updated.
  • the recursive update of the log likelihood ratio mean is performed.
  • the error probability of the i-th bit channel of the Polar code is obtained.
  • Q(*) represents a Q function commonly used in communication.
  • the Q function can be defined as
  • An encoding apparatus 500 according to an embodiment of the present invention will be described with reference to FIG. 5, and the encoding apparatus 500 includes:
  • a determining module 501 configured to determine N bits to be encoded, where N is a positive integer
  • An obtaining module 502 configured to acquire a first sequence that includes N polarization channel numbers
  • the determining module 501 is further configured to determine, according to the first sequence, a position of information bits in the N to-be-coded bits;
  • the encoding module 503 is configured to perform Polar coding on the N to-be-coded bits to obtain coded bits.
  • the determining module 501 is specifically configured to:
  • the obtaining module 502 is specifically configured to:
  • a first sequence comprising N polarized channel sequences is obtained from the sequence in Table 1 of the Appendix or the equivalent replacement sequence of the sequence in Table 1.
  • the determining module 501 is specifically configured to:
  • N N according to M, where symbol Indicates rounding down, the M is the target code length of the Polar code output, the M is not equal to the positive power of 2, and M is a positive integer.
  • the N to be encoded bits correspond to a mother code whose code length is N
  • the obtaining module 502 is specifically configured to:
  • the first sequence of the communication system supports a maximum of the first sequence S max maximum base code length N max corresponds to a first determined sequence of the mother code corresponding to the code length N, wherein the mother code corresponding to the code length N
  • the maximum first sequence S max is one of the sequence in the Appendix Table 1 or the equivalent replacement sequence in the sequence in Table 1, and the N bits to be coded correspond to N coded bits;
  • the obtaining module 502 is specifically configured to:
  • the N to be encoded bits correspond to a mother code whose code length is N
  • the obtaining module 502 is specifically configured to:
  • the first sequence corresponding to N is the first sequence including the N polarization channel numbers.
  • the fourth sequence is one of the sequence in Table 1 in the Appendix or the equivalent replacement sequence in the sequence in Table 1, and the N bits to be coded correspond to N coded bits;
  • the obtaining module 502 is specifically configured to:
  • the obtaining module 502 is specifically configured to:
  • a first sequence comprising N polarized channel sequences is obtained from the sequence in Table 2, Table 3 or Table 4 of the Appendix or the equivalent replacement sequence of the sequence in Table 2, Table 3 or Table 4.
  • the obtaining module 502 is specifically configured to:
  • a second sequence of N S 1, S 2, ..., S N is determined first sequence S 'N, a second sequence comprising i i S polarizations channel number, 1 ⁇ i ⁇ N, i is a positive integer.
  • the obtaining module 502 is specifically configured to:
  • the first sequence S' N is calculated based on the following formula:
  • FIG. 6 is a schematic structural diagram of a communication device 600 according to an embodiment of the present invention (for example, an access point or a base station, a communication device such as a station or a terminal, or a chip in the foregoing communication device, etc.).
  • a communication device 600 for example, an access point or a base station, a communication device such as a station or a terminal, or a chip in the foregoing communication device, etc.
  • communication device 600 can be implemented by bus 601 as a general bus architecture.
  • bus 601 can include any number of interconnecting buses and bridges.
  • Bus 601 connects various circuits together, including processor 602, storage medium 603, and bus interface 604.
  • the communication device 600 connects the network adapter 605 or the like via the bus 601 using the bus interface 604.
  • the network adapter 605 can be used to implement signal processing functions of the physical layer in the wireless communication network and to transmit and receive radio frequency signals through the antenna 607.
  • the user interface 606 can be connected to a user terminal such as a keyboard, display, mouse or joystick.
  • Bus 601 can also be connected to various other circuits, such as timing sources, peripherals, voltage regulators, or power management circuits, etc., which are well known in the art and therefore will not be described in detail.
  • the communication device 600 can also be configured as a general purpose processing system, such as generally referred to as a chip, the general purpose processing system including: one or more microprocessors providing processor functionality; and an external memory providing at least a portion of the storage medium 603 All of this is connected to other support circuits through an external bus architecture.
  • a general purpose processing system such as generally referred to as a chip, the general purpose processing system including: one or more microprocessors providing processor functionality; and an external memory providing at least a portion of the storage medium 603 All of this is connected to other support circuits through an external bus architecture.
  • the communication device 600 can be implemented using an ASIC (application specific integrated circuit) having a processor 602, a bus interface 604, a user interface 606, and at least a portion of the storage medium 603 integrated in a single chip, or Communication device 600 can be implemented using one or more FPGAs (Field Programmable Gate Arrays), PLDs (Programmable Logic Devices), controllers, state machines, gate logic, discrete hardware components, any other suitable circuitry, Or any combination of circuits capable of performing the various functions described throughout the present invention.
  • FPGAs Field Programmable Gate Arrays
  • PLDs Programmable Logic Devices
  • controllers state machines, gate logic, discrete hardware components, any other suitable circuitry, Or any combination of circuits capable of performing the various functions described throughout the present invention.
  • the processor 602 is responsible for managing the bus and general processing (including executing software stored on the storage medium 1203).
  • Processor 602 can be implemented using one or more general purpose processors and/or special purpose processors. Examples of processors include microprocessors, microcontrollers, DSP processors, and other circuits capable of executing software.
  • Software should be interpreted broadly to mean instructions, data, or any combination thereof, whether referred to as software, firmware, middleware, microcode, hardware description language, or otherwise.
  • Storage medium 603 is shown separated from processor 602 in the following figures, however, it will be readily apparent to those skilled in the art that storage medium 603, or any portion thereof, can be located external to communication device 600.
  • storage medium 603 can include transmission lines, carrier waveforms modulated with data, and/or computer products separate from wireless nodes, all of which can be accessed by processor 602 via bus interface 604.
  • storage medium 603, or any portion thereof, may be integrated into processor 602, for example, may be a cache and/or a general purpose register.
  • the processor 602 can be implemented in the foregoing embodiment, for example, FIG. 3a, FIG. 3b, FIG. 3c, FIG. 3d, FIG. 4a, and FIG. 4b sequentially corresponding to the first embodiment, the second embodiment, the third embodiment, and the fourth embodiment. For example 5 and embodiment 6, the execution process of the processor 602 will not be described herein.
  • the communication device in the embodiment of the present application may be a wireless communication device such as an access point, a station, a base station, or a user terminal.
  • the Polar code in the embodiment of the present application may also be a CA-Polar code or a PC-Polar code.
  • Arikan Polar refers to the original Polar code, which is not cascaded with other codes, only information bits and frozen bits.
  • the CA-Polar code is a Polar code cascading a Cyclic Redundancy Check (CRC) Polar code
  • the PC-Polar code is a Polar code cascading Parity Check (PC) code.
  • PC-Polar and CA-Polar improve the performance of Polar codes by cascading different codes.
  • the “information bit sequence” in the embodiment of the present application may also be called “bit sequence to be encoded” or “information bit set”.
  • the “number of information bits” may be the number of bits to be encoded in the bit sequence to be encoded. Number, or the number of elements in the information bit set.
  • the unit and method processes of the examples described in the embodiments of the present application can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the solution. The skilled person can use different methods for each particular application to implement the described functionality.
  • the disclosed apparatus and method may be implemented in other manners.
  • the device embodiments described above are merely illustrative.
  • the division of the unit is only a logical function division, and the actual implementation may have another division manner.
  • multiple units or components may be combined or integrated into another system, or some steps may be omitted or not performed.
  • the coupling or direct coupling or communication connection of the various units to each other may be through some interfaces, which may be in electrical, mechanical or other form.
  • the units described as separate components may or may not be physically separate, and may be located in one place or on multiple network elements.
  • each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.
  • the above embodiments it may be implemented in whole or in part by software, hardware, firmware, or any combination thereof.
  • software it may be implemented in whole or in part in the form of a computer program product.
  • the computer program product includes one or more computer instructions.
  • the computer program instructions When the computer program instructions are loaded and executed on a computer, the processes or functions described in accordance with embodiments of the present invention are generated in whole or in part.
  • the computer can be a general purpose computer, a special purpose computer, a computer network, or other programmable device.
  • the computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions can be from a website site, computer, server or data center Transfer to another website site, computer, server, or data center by wire (eg, coaxial cable, fiber optic, digital subscriber line (DSL), or wireless (eg, infrared, wireless, microwave, etc.).
  • the computer readable storage medium can be any available media that can be accessed by a computer or a data storage device such as a server, data center, or the like that includes one or more available media.
  • the usable medium may be a magnetic medium, such as a floppy disk, a hard disk, a magnetic tape, an optical medium such as a DVD, or a semiconductor medium such as a Solid State Disk (SSD).
  • SSD Solid State Disk

Abstract

本申请实施例提供一种编码方法、编码装置和通信装置。该方法包括：确定N个待编码比特，N为正整数；获取包含N个极化信道序号的第一序列；根据第一序列确定该N个待编码比特中信息比特的位置；对该N个待编码比特进行Polar编码以得到编码比特，基于获取的包含N个极化信道序号的第一序列来确定待编码比特中信息比特的位置，可以提高Polar码的性能。

Description

编码方法、编码装置和通信装置
本申请要求于2017年1月26日提交中国专利局、申请号为201710061840.2、发明名称为“编码方法、编码装置和通信装置”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本发明实施例涉及通信领域，并且更具体地，涉及编码方法、编码装置和通信装置。
背景技术
通信系统通常采用信道编码提高数据传输的可靠性，以保证通信的质量。土耳其教授Arikan提出的极化码(Polar codes)是第一个理论上证明可以达到香农容量且具有低编译码复杂度的好码。Polar码是一种线性块码，其编码矩阵为G N，例如，编码过程为
Figure PCTCN2018073435-appb-000001
其中
Figure PCTCN2018073435-appb-000002
是一个二进制的行矢量，长度为N(即母码长度)；G N是一个N×N的矩阵，且
Figure PCTCN2018073435-appb-000003
定义为log 2N个矩阵F 2的克罗内克(Kronecker)乘积。
上述矩阵
Figure PCTCN2018073435-appb-000004
Polar码的编码过程中，
Figure PCTCN2018073435-appb-000005
中的一部分比特用来携带信息，称为信息比特，这些比特的索引的集合记作
Figure PCTCN2018073435-appb-000006
另外的一部分比特设置为收发端预先约定的固定值，称之为固定比特或冻结比特(frozen bits)，其索引的集合用
Figure PCTCN2018073435-appb-000007
的补集
Figure PCTCN2018073435-appb-000008
表示。Polar码的编码过程相当于：
Figure PCTCN2018073435-appb-000009
这里，GN.(A)是GN.中由集合A中的索 引对应的那些行得到的子矩阵，GN(AC)是GN中由集合AC中的索引对应的那些行得到的子矩阵。
Figure PCTCN2018073435-appb-000010
为
Figure PCTCN2018073435-appb-000011
中的信息比特集合，信息比特个数为K；
Figure PCTCN2018073435-appb-000012
为
Figure PCTCN2018073435-appb-000013
中的固定比特集合，固定比特个数为(N-K)，是已知比特。这些固定比特通常被设置为0，但是只要收发端预先约定，固定比特可以被任意设置。固定比特设置为0时，Polar码的编码输出可简
化为：
Figure PCTCN2018073435-appb-000014
是一个K×N的矩阵。
Polar码的构造过程即集合
Figure PCTCN2018073435-appb-000015
的选取过程，决定了Polar码的性能。Polar码的构造过程通常是，根据母码码长N确定共存在N个极化信道，分别对应编码矩阵的N个行，计算极化信道可靠度，将可靠度较高的前K个极化信道的索引作为集合A的元素，剩余(N-K)个极化信道对应的索引作为固定比特的索引集合
Figure PCTCN2018073435-appb-000016
的元素。集合A决定了信息比特的位置，集合
Figure PCTCN2018073435-appb-000017
决定了固定比特的位置。
从编码矩阵可以看出，原始Polar码(母码)的码长为2的整数次幂，在实际应用中一般需要通过速率匹配实现任意码长的Polar码，通常可以采用打孔(puncture)或缩短(shorten)的方式实现速率匹配。
常见的极化信道可靠度的度量有错误概率、信道容量和极化权重等，现有技术中有三种极化信道可靠度估计的方法，一种是计算每个极化信道的巴氏(Bhattacharyya)参数，该参数反应了极化信道的错误概率，然后选择K个最小的巴氏参数对应的极化信道放置信息比特，但是该方法只适用于二进制擦除信道，对于其他信道无法准确地进行可靠度估计，因此性能不高；另外两种分别是密度进化(Density evolution简称：DE)方法和高斯近似(Gaussion approximation，简称：GA)法。DE方法和GA方法的计算复杂度相对较高，不适用于在线计算，对于离线存储，DE方法和GA方法在计算可靠度的时候依赖于实际信道的参数速率匹配方式，码率以及调制方式，上述参数中的任何一项发生变化极化信道的可靠度估计结果也会发生变化，对应的信息比特的位置也发生变化，最终导致存储的开销过大。
发明内容
本申请实施例提供编码方法、编码装置及通信装置，能够降低Polar码编码的存储复杂度以及提高Polar码的性能。
第一方面，提供一种编码方法，包括：
确定N个待编码比特，N为正整数；
获取包含N个极化信道序号的第一序列；
根据所述第一序列确定所述N个待编码比特中信息比特的位置；
对所述N个待编码比特进行Polar编码以得到编码比特。
结合第一方面，在第一方面的第一种可能的实现方式中，所述确定N个待编码比特包括：
根据M确定N,其中，N＝M，所述M为Polar码输出的目标码长，所述M等于2的正整数次幂，M为正整数。
结合第一方面的第一种可能的实现方式中，在第一方面的第二种可能的实现方式中，所述获取包含N个极化信道序号的第一序列包括：
从附录表1中序列或表1中序列的等同替换序列得到包含N个极化信道序列的第一序列。
结合第一方面，在第一方面的第三种可能的实现方式中，所述确定N个待编码比特包括：
根据M确定N,其中，
Figure PCTCN2018073435-appb-000018
符号
Figure PCTCN2018073435-appb-000019
表示向下取整，所述M为Polar码输出的目标码长，所述M不等于2的正整数次幂，M为正整数。
结合第一方面的第三种可能的实现方式中，在第一方面的第四种可能的实现方式中，所述N个待编码比特对应码长为N的母码，
所述获取包含N个极化信道序号的第一序列包括：
根据通信系统支持的最大母码码长N max对应的最大第一序列S max确定所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
结合第一方面的第四种可能的实现方式中，在第一方面的第五种可能的实现方式中，所述最大第一序列S max为附录表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
所述获取包含N个极化信道序号的第一序列包括：
确定所述N个编码比特中要删除的N-M个比特的位置；
依次读取所述最大第一序列S max中极化信道序号，并且将所述最大第一序列S max中不在所述N-M个比特的位置且不大于N的极化信道序号依次读出；
当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为所述母码码长N所对应的所述第一序列。
结合第一方面的第三种可能的实现方式中，在第一方面的第六种可能的实现方式中，所述N个待编码比特对应码长为N的母码，
所述获取包含N个极化信道序号的第一序列包括：
根据在无需进行速率匹配时所述母码码长N所对应的第四序列，确定在需要进行速率匹配时所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
结合第一方面的第六种可能的实现方式中，在第一方面的第七种可能的实现方式中，所述第四序列为附录中表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
所述根据母码码长N在无需进行速率匹配时所对应的第四序列，确定所述母码码长N所对应的第一序列包括：
确定所述N个编码比特中要删除的N-M个比特的位置；
依次读取第四序列中极化信道序号，并且将第四序列中不在所述N-M个比特的位置的极化信道序号依次读出；
当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为所述母码码长N在需要进行速率匹配时所对应的第一序列。
结合第一方面的第三种可能的实现方式中，在第一方面的第八种可能的实现方式中，所述获取包含N个极化信道序号的第一序列包括：
从附录中表2、表3或表4中序列或者所述表2、表3或表4中序列的等同替换序列得到包含N个极化信道序列的第一序列。
结合第一方面及其上述实现方式，在第一方面的第九种可能的实现方式中，所述获取包含N个极化信道序号的第一序列包括：
根据N个第二序列S 1，S 2，…,S N确定第一序列S′ N，第二序列S i包含i个极化信道序号，1≤i≤N，i为正整数。
结合第一方面的第九种可能的实现方式中，在第一方面的第十种可能的实现方式中，所述根据N个第二序列S 1，S 2，…,S N确定第一序列S′ N包括：
确定N个第二序列S 1，S 2，…,S N；
初始化第一序列S′ 1＝S 1；
设置j从2遍历到N，基于如下公式计算得到第一序列S′ N：
S′ j＝S′ j-1+(S′ j-1\S j)
其中，2≤j≤N，j为正整数，“\”表示计算两个序列的差集，“+”表示将前后两个序列进行连接以形成一个序列。
第二方面，提供一种编码装置，包括：
确定模块，用于确定N个待编码比特，N为正整数；
获取模块，用于获取包含N个极化信道序号的第一序列；
所述确定模块，还用于根据所述第一序列确定所述N个待编码比特中信息比特的位置；
所述编码模块，用于对所述N个待编码比特进行Polar编码以得到编码比特。
结合第二方面，在第二方面的第一种可能的实现方式中，所述确定模块具体用于：
根据M确定N,其中，N＝M，所述M为Polar码输出的目标码长，所述M等于2的正整数次幂，M为正整数。
结合第二方面的第一种可能的实现方式，在第二方面的第二种可能的实现方式中，所述获取模块具体用于：
从附录表1中序列或表1中序列的等同替换序列得到包含N个极化信道序列的第一序列。
结合在第二方面，在第二方面的第三种可能的实现方式中，所述确定模块具体用于：
根据M确定N,其中，
Figure PCTCN2018073435-appb-000020
符号
Figure PCTCN2018073435-appb-000021
表示向下取整，所述M为Polar码输出的目标码长，所述M不等于2的正整数次幂，M为正整数。
结合在第二方面的第三种可能的实现方式，在第二方面的第四种可能的实现方式中，所述N个待编码比特对应码长为N的母码，
所述获取模块具体用于：
根据通信系统支持的最大母码码长N max对应的最大第一序列S max确定所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
结合在第二方面的第四种可能的实现方式，在第二方面的第五种可能的实现方式中，所述最大第一序列S max为附录表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
所述获取模块具体用于：
确定所述N个编码比特中要删除的N-M个比特的位置；
依次读取所述最大第一序列S max中极化信道序号，并且将所述最大第一序列S max中不在所述N-M个比特的位置且不大于N的极化信道序号依次读出；
当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为所述母码码长N所对应的所述第一序列。
结合在第二方面的第三种可能的实现方式，在第二方面的第六种可能的实现方式中，所述N个待编码比特对应码长为N的母码，
所述获取模块具体用于：
根据在无需进行速率匹配时所述母码码长N所对应的第四序列，确定在需要进行速率匹配时所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
结合在第二方面的第六种可能的实现方式，在第二方面的第七种可能的实现方式中，所述第四序列为附录中表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
所述获取模块具体用于：
确定所述N个编码比特中要删除的N-M个比特的位置；
依次读取第四序列中极化信道序号，并且将第四序列中不在所述N-M个比特的位置的极化信道序号依次读出；
当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为所述母码码长N在需要进行速率匹配时所对应的第一序列。
结合在第二方面的第三种可能的实现方式，在第二方面的第八种可能的实现方式中，所述获取模块具体用于：
从附录中表2、表3或表4中序列或者所述表2、表3或表4中序列的等同替换序列得到包含N个极化信道序列的第一序列。
结合在第二方面及其上述实现方式，在第二方面的第九种可能的实现方式中，所述获取模块具体用于：
根据N个第二序列S 1，S 2，…,S N确定第一序列S′ N，第二序列S i包含i个极化信道序号，1≤i≤N，i为正整数。
结合在第二方面的第九种可能的实现方式，在第二方面的第十种可能的实现方式中，所述获取模块具体用于：
确定N个第二序列S 1，S 2，…,S N；
初始化第一序列S′ 1＝S 1；
设置j从2遍历到N，基于如下公式计算得到第一序列S′ N：
S′ j＝S′ j-1+(S′ j-1\S j)
其中，2≤j≤N，j为正整数，“\”表示计算两个序列的差集，“+”表示将前后两个序列进行连接以形成一个序列。
第三方面，提供一种通信装置，包括：
存储器，用于存储程序；
处理器，用于执行所述存储器存储的所述程序，当所述程序被执行时，所述处理器用于执行上述第一方面或第一方面的任意一种可能的实现方式。
本申请的又一方面提了供一种计算机可读存储介质，所述计算机可读存储介质中存储有指令，当其在计算机上运行时，使得计算机执行上述各方面所述的方法。
本申请的又一方面提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得计算机执行上述各方面所述的方法。
本申请的又一方面提供了一种计算机程序，当其在计算机上运行时，使得计算机执行上述各方面所述的方法。
本申请实施例中，基于获取的包含N个极化信道序号的第一序列来确定待编码比特中信息比特的位置，可以提高Polar码的性能。
附图说明
图1是本申请提供的无线通信系统的结构；
图2a是无线通信发送端和接收端的基本流程示意图；
图2b是本申请实施的Polar码的编码过程示意图；
图3a是本申请实施的一种编码方法流程示意图；
图3b是图3a中步骤302的又一种实施方式流程图；
图3c是图3a中步骤302的又一种实施方式流程图；
图3d是图3a中步骤302的又一种实施方式流程图；
图4a是本申请实施的另一种编码方法流程示意图；
图4b是图4a中步骤402的又一种实施方式流程图；
图5是本申请实施的编码装置结构图；
图6是本申请实施的通信装置结构图。
具体实施方式
本发明实施例可应用于各种通信系统，因此，下面的描述不限制于特定通信系统。全球移动通讯(Global System of Mobile communication，简称“GSM”)系统、码分多址(Code Division Multiple Access，简称“CDMA”)系统、宽带码分多址(Wideband Code Division Multiple Access，简称“WCDMA”)系统、通用分组无线业务(General Packet Radio Service，简称“GPRS”)、长期演进(Long Term Evolution，简称“LTE”)系统、LTE频分双工(Frequency Division Duplex，简称“FDD”)系统、LTE时分双工(Time Division Duplex， 简称“TDD”)、通用移动通信系统(Universal Mobile Telecommunication System，简称“UMTS”)等。在上述的系统中的基站或者终端使用传统Turbo码、LDPC码编码处理的信息或者数据都可以使用本实施例中的Polar码编码。
在本说明书中使用的术语“部件”、“模块”、“系统”等用于表示计算机相关的实体、硬件、固件、硬件和软件的组合、软件、或执行中的软件。例如，部件可以是但不限于，在处理器上运行的进程、处理器、对象、可执行文件、执行线程、程序和/或计算机。通过图示，在计算设备上运行的应用和计算设备都可以是部件。一个或多个部件可驻留在进程和/或执行线程中，部件可位于一个计算机上和/或分布在两个或更多个计算机之间。此外，这些部件可从在上面存储有各种数据结构的各种计算机可读介质执行。部件可例如根据具有一个或多个数据分组(例如来自与本地系统、分布式系统和/或网络间的另一部件交互的二个部件的数据，例如通过信号与其它系统交互的互联网)的信号通过本地和/或远程进程来通信。
此外，结合接入终端描述了各个实施例。接入终端也可以称为系统、用户单元、用户站、移动站、移动台、远方站、远程终端、移动设备、用户终端、终端、无线通信设备、用户代理、用户装置或UE(User Equipment，用户设备)。接入终端可以是蜂窝电话、无绳电话、SIP(Session Initiation Protocol，会话启动协议)电话、WLL(Wireless Local Loop，无线本地环路)站、PDA(Personal Digital Assistant，个人数字处理)、具有无线通信功能的手持设备、计算设备或连接到无线调制解调器的其它处理设备。此外，结合基站描述了各个实施例。基站可用于与移动设备通信，基站可以是GSM(Global System of Mobile communication，全球移动通讯)或CDMA(Code Division Multiple Access，码分多址)中的BTS(Base Transceiver Station，基站)，也可以是WCDMA(Wideband Code Division Multiple Access，宽带码分多址)中的NB(NodeB，基站)，还可以是LTE(Long Term Evolution，长期演进)中的eNB或eNodeB(Evolutional Node B，演进型基站)，或者中继站或接入点，或者未来5G网络中的基站设备等。
现在，参照图1，示出根据本文所述的各个实施例的无线通信系统100。系统100包括基站102，后者可包括多个天线组。例如，一个天线组可包括天线104和106，另一个天线组可包括天线108和110，附加组可包括天线112和114。对于每个天线组示出了2个天线，然而可对于每个组使用更多或更少的天线。基站102可附加地包括发射机链和接收机链，本领域普通技术人员可以理解，它们均可包括与信号发送和接收相关 的多个部件(例如处理器、调制器、复用器、解调器、解复用器或天线等)。
基站102可以与一个或多个接入终端(例如接入终端116和接入终端122)通信。然而，可以理解，基站102可以与类似于接入终端116和122的基本上任意数目的接入终端通信。接入终端116和122可以是例如蜂窝电话、智能电话、便携式电脑、手持通信设备、手持计算设备、卫星无线电装置、全球定位系统、PDA和/或用于在无线通信系统100上通信的任意其它适合设备。如图所示，接入终端116与天线112和114通信，其中天线112和114通过前向链路118向接入终端116发送信息，并通过反向链路120从接入终端116接收信息。此外，接入终端122与天线104和106通信，其中天线104和106通过前向链路124向接入终端122发送信息，并通过反向链路126从接入终端122接收信息。在FDD(Frequency Division Duplex，频分双工)系统中，例如，前向链路118可利用与反向链路120所使用的不同频带，前向链路124可利用与反向链路126所使用的不同频带。此外，在TDD(Time Division Duplex，时分双工)系统中，前向链路118和反向链路120可使用共同频带，前向链路124和反向链路126可使用共同频带。
被设计用于通信的每组天线和/或区域称为基站102的扇区。例如，可将天线组设计为与基站102覆盖区域的扇区中的接入终端通信。在通过前向链路118和124的通信中，基站102的发射天线可利用波束成形来改善针对接入终端116和122的前向链路118和124的信噪比。此外，与基站通过单个天线向它所有的接入终端发送相比，在基站102利用波束成形向相关覆盖区域中随机分散的接入终端116和122发送时，相邻小区中的移动设备会受到较少的干扰。
在给定时间，基站102、接入终端116和/或接入终端122可以是发送无线通信装置和/或接收无线通信装置。当发送数据时，发送无线通信装置可对数据进行编码以用于传输。具体地，发送无线通信装置可具有(例如生成、获得、在存储器中保存等)要通过信道发送至接收无线通信装置的一定数目的信息比特。这种信息比特可包含在数据的传输块(或多个传输块)中，其可被分段以产生多个代码块。此外，发送无线通信装置可使用Polar码编码器(未示出)来对每个代码块编码。
图2a是无线通信的基本流程，在发送端，信源依次经过信源编码、信道编码、数字调制后发出。在接收端，依次通过数字解调、信道解码、信源解码输出信宿。信道编解码可以采用Polar码，由于原始Polar码(母码)的码长为2的整数次幂，在实际应用中需要通过速率匹配实现任意码长的Polar码。图2a所示的，在发送端在信道编码后进行速率匹配实现任意的目标码长，在接收端，信道解码之前先进行解速率匹配。
如图2b所示，Polar码的编码过程包括构造、编码和速率匹配三个处理过程。
首先是构造过程：接收输入的N1个信息比特，根据母码码长N确定与母码码长N对应的序列，其中，母码码长N根据编码后的目标码长M确定，待编码的比特的个数为N，N个待编码的比特包括N1个信息比特和N2个固定比特，根据信息比特的数目从该序列中确定信息比特的位置，也即确定出固定比特的位置；然后是编码过程：对待编码的比特进行Polar编码，获得Polar编码后的比特；最后是速率匹配过程：由于Polar码编码后的码长(即母码码长)为2的正整数次幂，而实际应用中一般需要通过速率匹配 实现任意码长的Polar码，通常可以采用打孔(puncture)或缩短(shorten)的方案实现速率匹配，具体实现是删掉2的正整数次幂的码长中的部分N-M个比特，得到目标码长，其中N、M、N1、N2均为正整数。
本发明实施例提供的编码方法涉及图2b所示的Polar码编码过程，最主要涉及构造过程，即如何确定信息比特的位置。本发明实施例提供一种编码方法，基于获取的包含N个极化信道序号的第一序列来确定待编码比特中信息比特的位置，可以提高Polar码的性能。
由于Polar码编码后的母码码长为2的正整数次幂，而Polar码输出的目标码长可以为2的正整数次幂或不为2的正整数次幂，在Polar码输出的目标码长为2的正整数次幂时，无需进行速率匹配；在Polar码输出的目标码长不为2的正整数次幂时，则需要进行速率匹配。
图3a描述了一种编码法方法流程300，下面结合图3a来详细描述如下各个实施例。
实施例一
该实施例所提供的编码方法包括：
S301、确定N个待编码比特。
其中，N＝M，M作为Polar码输出的目标码长等于2的正整数次幂，M为正整数；N个待编码比特对应N个极化信道，一个比特对应一个极化信道。
S302、获取包含N个极化信道序号的第一序列。
在本发明的一个实施例中，附录表1给出了N在取不同值时所对应的第一序列。表1中N为待编码比特长度，表格中的各个第一序列中的元素为极化信道的序号。表1的全部或者部分第一序列可以存储在应用本实施方式的通信系统中。
需要说明的是，表1以及后续实施例中涉及到的表2、表3和表4，仅仅为举例，在不影响其整体效果的前提下，对于表1、表2、表3和表4中的序列可以做包括但不限于如下几方面的调整或者等同替换：
1、表1、表2、表3和表4中各个第一序列中少数元素之间的位置互换。例如，各个第一序列中间隔不超过10的两个元素之间的位置进行互换；
2、表1、表2、表3和表4中各个第一序列中包含从1开始到N结束的N个元素，N为母码码长，从1开始到N结束的N个元素代表N个极化信道的序号。实际上，N个极化信道的序号也可以从0开始到N-1结束，因此，将目前附录中表1、表2、表3和表4中各个第一序列中各个元素减去1即可形成包含从0开始到N-1结束的N个元素。当然，也可以采取其他方式表示上述极化信道的序号或者标识，该具体表达方式不影响表格中所表示的极化信道的具体位置。
3、表1、表2、表3和表4中各个第一序列中的元素可以逆序。
S303、基于第一序列确定N个待编码比特中信息比特的位置。
具体地，在该第一序列中取前K个或后K个极化信道序号所对应的极化信道的位置作为信息比特的位置，其他极化信道位置作为固定比特的位置，从而得到信息比特和固定比特的位置，其中，K为N个待编码比特中信息比特的个数，K为小于N的正整数。
需要说明的是，本实施例并不限制一定取第一序列中前K个或后K个极化信道序号所对应的极化信道的位置作为信息比特的位置。
进一步，第一序列确定的信息比特的位置满足包含关系，即，确定出K个信息比特位置的集合是K+m个信息比特位置的集合的子集，其中，m为正整数，从而降低Polar码编码的存储复杂度。
S304、对N个待编码比特进行Polar编码以得到编码比特。
具体地，可以使用Polar码的编码矩阵F N完成待编码比特的编码过程，进而得到Polar编码后的编码比特。
上述实施方式与其他实施方式相比，不同主要在于步骤S302，这样通信系统中通过存储第一序列S大大减小构造第一序列的计算复杂度。
实施例二
在本发明的另一个实施例中，实施例一中S302中所述的第一序列，替换的，可以根据N个第二序列S 1，S 2，…，S N生成第一序列S′ N，第二序列S i包含i个极化信道的序号，即包含i个元素，且第二序列S i基于N个极化信道的可靠度确定，1≤i≤N，i为正整数。
具体地，如图3b所示，S302a：根据N个第二序列S 1，S 2，…，S N生成第一序列S′ N包括：
S302a1、确定N个第二序列S 1，S 2，…,S N；针对第二序列S i，1≤i≤N，第二序列S i的确定过程为：
确定N个极化信道的可靠度；
根据所述N个极化信道的可靠度确定第二序列S i，其中，第二序列S i中包含i个极化信道序号，该i个极化信道序号对应i个极化信道，该i个极化信道中任一极化信道的可靠度大于该N个极化信道中除该i个极化信道之外的(N-i)个极化信道的可靠度。
需要说明的是，第二序列S i中所包含的i个元素(即i个极化信道序号)可以按照极化信道的可靠度进行排序，也可以不按照极化信道的可靠度进行排序，即其可以是一个没有排序的集合。
例如，针对第二序列S 1，确定N个极化信道的可靠度，将确定出的N个极化信道的可靠度中最大可靠度所对应的极化信道的序号做组成的序列作为第二序列S 1，即S 1中包含最大可靠度所对应的极化信道的序号，并且由于S 1中包含一个元素，因此，S 1中所包含的元素不存在排序的概念。
常见的极化信道的可靠度的度量有错误概率、信道容量和极化权重等，例如，可以利用高斯近似算法或密度进化算法来确定极化信道的可靠度。本发明对于采用何种算法来确定极化信道的可靠度不做限定。
S302a2、初始化第一序列S′ 1＝S 1；
S302a3、计算第一序列S′ i
具体的，采用如下公式计算第一序列S′ i：
S′ j＝S′ j-1+(S′ j-1\S j)
其中，2≤j≤N，j为正整数，\表示计算两个序列的差集，例如，序列[1 2 3]\[1 3 2 4]为[4]，“+”表示将前后两个序列连接以形成一个序列，例如，[3 2 1]+[4]为[3 2 1 4]。
j依次从2遍历到N，进而得到第一序列S′ N。
本实施方式中，其他步骤S301a、S303a、S304a可以分别参考前述S301、S303、S304，此处不再赘述。该实施方式与其他实施方式相比，不同主要在于步骤S302a，这样通信系统中通过不需要存储第一序列大大节约了存储资源。
实施例三
在本发明的又一个实施例中，可以根据通信系统支持的最大母码码长N max对应的最大第一序列S max，确定当前母码码长N对应的第一序列S。
该最大第一序列S max可以是协议约定的，存储在通信系统中，例如，最大第一序列S max可以是实施例一中表1中的N位于256和1024之间，或者1024与2048之间时所对应的某个第一序列，也可以是根据实施例二中生成方法生成并存储的第一序列。
需要补充说明的是，目前Polar码的最大母码码长(Maximum mother code size of Polar code)可以为:
256≤N max≤1024(针对下行控制信息)
1024≤N max≤2048(针对上行控制信息)。
当当前母码码长N等于Nmax时，本实施方式等同于前述S301至S304或S301a至S304a，此处不再赘述。
当N小于N max时，如图3c所示，该实施方式包括：
S301b、确定N个待编码比特。
其中，N<N max且
Figure PCTCN2018073435-appb-000022
M作为Polar码的非最大目标码长不等于2的正整数次幂，M为正整数。
此时，N个待编码比特对应码长为N的当前母码，N作为当前母码码长小于最大母码码长N，且当前母码码长N需要经过速率匹配以得到目标码长M。
S302b、获取包含N个极化信道序号的第一序列。
具体地，根据通信系统支持的最大母码码长N max对应的最大第一序列S max，确定当前母码码长N对应的第一序列，具体包括：
S302b1、获取最大母码码长N max对应的最大第一序列S max。
如前文所述，可以直接从存储器中获取该最大第一序列S max，最大第一序列S max可以是协议约定的，存储在通信系统中，例如，最大第一序列S max可以是实施例一中表1中的N位于256和1024之间，或者1024与2048之间时所对应的某个第一序列，也可以是根据实施例二中生成方法生成并存储的第一序列。
S302b2、确定N个编码中要删除的N-M个比特的位置，其中，N个待编码比特对应该N个编码比特；
由于当前母码码长N需要经过速率匹配以得到目标码长M，通常可以采用打孔模式 中打孔位置或缩短(shorten)模式中shorten位置实现速率匹配，因此，要删除的N-M个比特的位置可以是打孔模式中打孔位置或缩短(shorten)模式中shorten位置，其中，打孔模式可以是从前往后或从前往后的比特逆序，shorten模式可以是从后往前或从后往前的比特逆序。
下面将分别描述打孔位置或shorten位置：
1、打孔位置
1)从前往后
前面N-M个比特的位置设置为0，其他比特的位置设置为1，即
Figure PCTCN2018073435-appb-000023
其中，“0”表示打孔位置，“1”表示未打孔位置。
2)从前往后的比特逆序
对从前往后的打孔位置进行比特逆序，比特逆序是指把一个十进制整数转换成二进制形式，把二进制元素的顺序取反，把取反后的二进制数转换成十进制，新得到的数即是原数的比特逆序值。
具体地，初始化长度为N的辅助序列(即从前往后的打孔位置)，设置前N-M个元素为0，后M个元素为1，N表示母码码长，M表示目标码长，其中，其中，“0”表示打孔位置，“1”表示未打孔位置，该辅助序列为：
Figure PCTCN2018073435-appb-000024
对该辅助序列
Figure PCTCN2018073435-appb-000025
进行比特逆序重排，得到打孔模式
Figure PCTCN2018073435-appb-000026
即为从前往后的比特逆序打孔模式，其中
Figure PCTCN2018073435-appb-000027
D(b 1b 2...b n)将二进制序列b 1b 2...b n转换成十进制数，
Figure PCTCN2018073435-appb-000028
2、shorten位置
1)从后往前
后面N-M个比特的位置设置为0，其他比特的位置设置为1，即
Figure PCTCN2018073435-appb-000029
其中，“0”表示shorten位置，“1”表示非shorten位置。
2)从后往前的比特逆序
对从后往前的shorten位置进行比特逆序。
具体地，初始化长度为N的辅助序列，设置前M个元素为1，后N-M个元素为0，N表示母码码长，M表示目标码长，该辅助序列为：
Figure PCTCN2018073435-appb-000030
对
Figure PCTCN2018073435-appb-000031
进行比特逆序重排，得到打孔模式
Figure PCTCN2018073435-appb-000032
其中“0”所在位置的编码比特被shorten，其中
Figure PCTCN2018073435-appb-000033
其中，D(b 1b 2...b n)将二进制序列b 1b 2...b n转换成十进制数，
Figure PCTCN2018073435-appb-000034
S302b3、依次读取最大第一序列S max中极化信道序号，并且将最大第一序列S max中不在所述N-M个比特的位置且不大于N的极化信道序号依次读出；
S302b4、当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为该非最大母码码长N所对应的第一序列。
S303b、基于该第一序列确定N个待编码比特中信息比特的位置。
具体地，可以取第一序列中前K个或后K个极化信道序号所对应的极化信道的位置作为信息比特的位置，其他极化信道位置作为固定比特的位置，其中，K为N个待编码比特中信息比特的个数。
S304b、对该N个待编码比特进行Polar编码以得到编码比特。
从该实施方式看出，该实施方式与其他实施方式相比，不同主要在于步骤S302b，这样，通信系统中仅需要存储最大第一序列S max，从而节省了存储空间，另外，第一序列的构造过程的计算复杂度也相对较低。
实施例四
在本发明的又一个实施例中，可以根据母码码长N在无需进行速率匹配时所对应的第四序列，确定同样的母码码长N在需要进行速率匹配时所对应的第一序列。
其中，母码码长N在无需进行速率匹配时所对应的第四序列可以是协议约定的，存储在通信系统中，例如，第四序列可以是实施例一表1中N在取不同的值时所对应的第一序列，也可以是根据实施例二中生成方法生成并存储的第一序列。
如下将描述母码码长N在需要进行速率匹配时如何确定对应的第一序列。如图3d 所示，该实施方式包括：
S301c、确定N个待编码比特。
其中，
Figure PCTCN2018073435-appb-000035
M作为Polar码的目标码长不等于2的正整数次幂，M为正整数。
此时，N个待编码比特对应码长为N的母码，母码码长N需要经过速率匹配以得到目标码长M。
S302c、获取包含N个极化信道序号的第一序列；
具体地，根据母码码长N在无需进行速率匹配时所对应的第四序列，确定母码码长N对应的第一序列，具体包括：
S302c1、获取母码码长N在无需进行速率匹配时所对应的第四序列。
如前文所述，母码码长N在无需进行速率匹配时所对应的第四序列可以是协议约定的，存储在通信系统中，例如，第四序列可以是实施例一表1中N在取不同的值时所对应的第一序列，也可以是根据实施例二中生成方法生成并存储的第一序列。
S302c2、确定N个编码比特中要删除的N-M个比特的位置，其中，N个待编码比特对应该N个编码比特。
由于母码码长N需要经过速率匹配以得到目标码长M，通常可以采用打孔模式中打孔位置或缩短(shorten)模式中shorten位置实现速率匹配，因此，要删除的N-M个比特的位置可以是打孔模式中打孔位置或缩短(shorten)模式中shorten位置，关于打孔位置或shorten位置可以参考前面相关描述。
S302c3、依次读取第四序列中极化信道序号，并且将第四序列中不在所述N-M个比特的位置的极化信道序号依次读出；
S302c4、当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为母码码长N在需要进行速率匹配时所对应的第一序列。
S303c、基于该第一序列确定N个待编码比特中信息比特的位置。
具体地，可以取第三序列中前K个或后K个极化信道序号所对应的极化信道的位置作为信息比特的位置，其他极化信道位置作为固定比特的位置，其中，K为N个待编码比特中信息比特的个数。
需要说明的是，本实施例并不限制一定取第一序列中前K个或后K个极化信道序号所对应的极化信道的位置作为信息比特的位置。
S304c、对该N个待编码比特进行Polar编码以得到编码比特。
具体地，可以使用Polar码的编码矩阵F N完成待编码比特的编码过程，进而得到Polar编码后的编码比特。
从该实施方式看出，该实施方式与其他实施方式相比，不同主要在于步骤S302c，这样，通信系统中仅需要存储母码码长N在无需进行速率匹配时所对应的第四序列，从而节省了存储空间，另外，母码码长N在需要进行速率匹配时所对应的第一序列的构造过程的计算复杂度也相对较低。
实施例五
与上述实施例四相比，在该实施例中，根据相关的附录中的表来确定母码码长N在需要进行速率匹配时所对应的第一序列。
图4a描述本发明另一个实施例提供的编码方法流程400，具体地，该编码流程包括：
S401、确定N个待编码比特，其中，
Figure PCTCN2018073435-appb-000036
M作为Polar码的目标码长不等于2正整数次幂，M为正整数。
此时，母码码长N需要经过速率匹配以得到目标码长M。
S402、获取包含N个极化信道序号的第一序列。
在本发明的一个实施例中，附录表2给出了M和N在取不同值时所对应的第一序列。表2中M为Polar码的目标码长，N为待编码比特的个数，各个第一序列中的元素为极化信道序号。
在本发明的又一个实施例中，附录表3给出了M和N在取不同值时所对应的第一序列。表3中M为Polar码的目标码长，N为待编码比特的个数，各个第一序列中的元素为极化信道序号。
在本发明的又一个实施例中，附录表4给出了M和N在取不同值时所对应的第一序列。表4中M为Polar码的目标码长，N为待编码比特的个数，各个第一序列中的元素为极化信道序号。
针对表2、表3和表4中序列的等同替换可以参见实施例一中相关描述。
S403、基于上述第一序列确定N个待编码比特中信息比特的位置。
具体地，在该第一序列中取前K个极化信道序号所对应的极化信道的位置作为信息比特的位置，其他极化信道位置作为固定比特的位置，从而得到信息比特和固定比特的位置，其中，K为N个待编码比特中信息比特的个数。
需要说明的是，本实施例并不限制一定取第一序列中前K个或后K个极化信道序号所对应的极化信道的位置作为信息比特的位置。
S404、对N个待编码比特进行Polar编码以得到编码比特。
具体地，可以使用Polar码的编码矩阵F N完成待编码比特的编码过程，进而得到Polar编码后的编码比特。
实施例六
与上述实施例五类似的，在本发明的又一个实施例中，根据根据N个第二序列S 1，S 2，…，S N来确定母码码长N在需要进行速率匹配时所对应的第一序列。
具体地，针对前述S402，替换的，可以根据N个第二序列S 1，S 2，…，S N确定第一序列，第二序列S i包含i个极化信道的序号，即包含i个元素，且第二序列S i基于N个极化信道的可靠度确定，1≤i≤N，i为正整数。
具体地，如图4b所示，S402a：根据N个第二序列S 1，S 2，…，S N确定第一序列包括：
S402a1、确定N个第二序列S 1，S 2，…,S N。
针对第二序列S i，1≤i≤N，第二序列S i的确定过程为：
确定N个极化信道的可靠度；
根据所述N个极化信道的可靠度确定第二序列S i，其中，第二序列S i中包含i个极 化信道序号，该i个极化信道序号对应i个极化信道，该i个极化信道中任一极化信道的可靠度大于该N个极化信道中除该i个极化信道之外的(N-i)个极化信道的可靠度。
需要说明的是，第二序列S i中所包含的i个元素(即i个极化信道序号)可以按照极化信道的可靠度进行排序，也可以不按照极化信道的可靠度进行排序，即其可以是一个没有排序的集合。
例如，针对第二序列S 1，确定N个极化信道的可靠度，将确定出的N个极化信道的可靠度中最大可靠度所对应的极化信道的序号做组成的序列作为第二序列S 1，即S 1中包含最大可靠度所对应的极化信道的序号，并且由于S 1中包含一个元素，因此，S 1中所包含的元素不存在排序的概念。
常见的极化信道的可靠度的度量有错误概率、信道容量和极化权重等，例如，可以利用高斯近似算法或密度进化算法来确定极化信道的可靠度。本发明对于采用何种算法来确定极化信道的可靠度不做限定。
通常可以采用打孔模式或缩短(shorten)模式来实现速率匹配，在打孔模式中打孔位置可以为从前往后或从前往后的比特逆序，在shorten模式中shorten位置可以为从后往前或从后往前的比特逆序，不同的打孔位置或shorten位置会导致确定出的极化信道的可靠度不同，进而产生不同的第二序列S i，例如，在高斯近似算法中，不同的打孔位置或shorten位置会影响初始化值，进而计算出不同的错误概率，关于在高斯近似算法中如何利用打孔位置或shorten位置来计算错误概率后面有进一步的描述。
S402a2、初始化第一序列S′ 1＝S 1；
S402a3、计算第一序列S′ i；
具体地，基于如下公式，计算第一序列S′ i：
S′ j＝S′ j-1+(S′ j-1\S j)
其中，2≤j≤N，j为正整数，\表示计算两个序列的差集，例如，序列[1 2 3]\[1 3 2 4]为[4]，“+”表示将前后两个序列连接以形成一个序列，例如，[3 2 1]+[4]为[3 2 1 4]。
j依次从2遍历到N，进而得到第一序列S′ N。
本实施方式中，其他步骤S401a、S403a、S404a可以分别参考前述S401、S403、S404，此处不再赘述。
上述实施方式与其他实施方式相比，不同主要在于步骤S402a，这样通信系统中通过不需要存储第一序列S大大节约了存储资源。
针对前述各个实施方式，下面将描述利用高斯近似算法计算N个极化信道的错误概率的过程：
1、对N个极化信道中每个极化信道对应的对数似然比均值进行初始化，以得到对数似然比均值的初始值。
对Polar码中的每个码符号位置，进行对应的对数似然比的初始化，得到各码符号位置的对数似然比均值初始值。
在图3对应实施例中，即无需速率匹配情形(无需打孔或shorten)，使用如下公式计算各码符号位置的对数似然比均值初始值。
Figure PCTCN2018073435-appb-000037
其中，
Figure PCTCN2018073435-appb-000038
表示第i个码符号位置的对数似然比均值初始值，σ用于指示信号的噪声。
在图4对应实施例中，即需要速率匹配情形，针对打孔模式或shorten模式分别提供不同的初始值。
在打孔模式中，使用如下公式计算各码符号位置的对数似然比均值初始值：
Figure PCTCN2018073435-appb-000039
其中，puncturingx(i)表示第i个码符号位置为打孔位置，Nopuncturingx(i)表示第i个码符号位置非打孔位置。x(i)表示第i个码符号位置，
Figure PCTCN2018073435-appb-000040
表示第i个码符号位置的对数似然比均值初始值，σ用于指示信号噪声的标准差。
在缩短(shorten)模式中，使用如下公式计算各码符号位置的对数似然比均值初始值：
Figure PCTCN2018073435-appb-000041
其中，shortingx(i)表示第i个码符号位置为shorten位置，NoShortingx(i)表示第i个码符号位置为非shorten位置。
2、在对数似然比均值的初始值的基础上，对对数似然比均值递归更新。
在上述计算出的对数似然比均值的初始值的基础上，进行该对数似然比均值的递归更新。
其使用的公式包括：
Figure PCTCN2018073435-appb-000042
Figure PCTCN2018073435-appb-000043
其中，公式一是对
Figure PCTCN2018073435-appb-000044
和
Figure PCTCN2018073435-appb-000045
进行了定义。
公式二涉及到了
Figure PCTCN2018073435-appb-000046
而
Figure PCTCN2018073435-appb-000047
可表示为：
Figure PCTCN2018073435-appb-000048
3，根据更新后的对数似然比均值得到N个极化信道的错误概率。
根据更新后的对数似然比均值，得到Polar码的第i个比特信道的错误概率。
其使用的公式包括：
Figure PCTCN2018073435-appb-000049
其中，p i表示第i个极化信道的错误概率，Q(*)表示通信中常用的Q函数，例如，Q函数可以定义为
Figure PCTCN2018073435-appb-000050
如下将结合图5来描述本发明实施例提供的编码装置500，编码装置500包括：
确定模块501，用于确定N个待编码比特，N为正整数；
获取模块502，用于获取包含N个极化信道序号的第一序列；
确定模块501，还用于根据所述第一序列确定所述N个待编码比特中信息比特的位 置；
编码模块503，用于对所述N个待编码比特进行Polar编码以得到编码比特。
在本发明的一个实施例中，确定模块501具体用于：
根据M确定N,其中，N＝M，所述M为Polar码输出的目标码长，所述M等于2的正整数次幂，M为正整数。
相应地，获取模块502具体用于：
从附录表1中序列或表1中序列的等同替换序列得到包含N个极化信道序列的第一序列。
在本发明的又一个实施例中，确定模块501具体用于：
根据M确定N,其中，
Figure PCTCN2018073435-appb-000051
符号
Figure PCTCN2018073435-appb-000052
表示向下取整，所述M为Polar码输出的目标码长，所述M不等于2的正整数次幂，M为正整数。
相应地，在该实施例的第一种可实施方式中，所述N个待编码比特对应码长为N的母码，获取模块502具体用于：
根据通信系统支持的最大母码码长N max对应的最大第一序列S max确定所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
进一步，所述最大第一序列S max为附录表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
获取模块502具体用于：
确定所述N个编码比特中要删除的N-M个比特的位置；
依次读取所述最大第一序列S max中极化信道序号，并且将所述最大第一序列S max中不在所述N-M个比特的位置且不大于N的极化信道序号依次读出；
当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为所述母码码长N所对应的所述第一序列。
相应地，在该实施例的第二种可实施方式中，所述N个待编码比特对应码长为N的母码，获取模块502具体用于：
根据在无需进行速率匹配时所述母码码长N所对应的第四序列，确定在需要进行速率匹配时所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
进一步，所述第四序列为附录中表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
获取模块502具体用于：
确定所述N个编码比特中要删除的N-M个比特的位置；
依次读取第四序列中极化信道序号，并且将第四序列中不在所述N-M个比特的位置的极化信道序号依次读出；
当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成 的序列为所述母码码长N在需要进行速率匹配时所对应的第一序列。
相应地，在该实施例的第三种可实施方式中，获取模块502具体用于：
从附录中表2、表3或表4中序列或者所述表2、表3或表4中序列的等同替换序列得到包含N个极化信道序列的第一序列。
在本发明的又一个实施例中，获取模块502具体用于：
根据N个第二序列S 1，S 2，…,S N确定第一序列S′ N，第二序列S i包含i个极化信道序号，1≤i≤N，i为正整数。
进一步，获取模块502具体用于：
确定N个第二序列S 1，S 2，…,S N；
初始化第一序列S′ 1＝S 1；
设置j从2遍历到N，基于如下公式计算得到第一序列S′ N：
S′ j＝S′ j-1+(S′ j-1\S j)
其中，2≤j≤N，j为正整数，“\”表示计算两个序列的差集，“+”表示将前后两个序列进行连接以形成一个序列。
图6为本发明实施例所提供的通信装置600的结构示意图(例如接入点或基站、站点或者终端等通信装置，或者前述通信装置中的芯片等)。
如下图6所示，通信装置600可以由总线601作一般性的总线体系结构来实现。根据通信装置600的具体应用和整体设计约束条件，总线601可以包括任意数量的互连总线和桥接。总线601将各种电路连接在一起，这些电路包括处理器602、存储介质603和总线接口604。可选的，通信装置600使用总线接口604将网络适配器605等经由总线601连接。网络适配器605可用于实现无线通信网络中物理层的信号处理功能，并通过天线607实现射频信号的发送和接收。用户接口606可以连接用户终端，例如：键盘、显示器、鼠标或者操纵杆等。总线601还可以连接各种其它电路，如定时源、外围设备、电压调节器或者功率管理电路等，这些电路是本领域所熟知的，因此不再详述。
可以替换的，通信装置600也可配置成通用处理系统，例如通称为芯片，该通用处理系统包括:提供处理器功能的一个或多个微处理器；以及提供存储介质603的至少一部分的外部存储器，所有这些都通过外部总线体系结构与其它支持电路连接在一起。
可替换的，通信装置600可以使用下述来实现:具有处理器602、总线接口604、用户接口606的ASIC(专用集成电路)；以及集成在单个芯片中的存储介质603的至少一部分，或者，通信装置600可以使用下述来实现：一个或多个FPGA(现场可编程门阵列)、PLD(可编程逻辑器件)、控制器、状态机、门逻辑、分立硬件部件、任何其它适合的电路、或者能够执行本发明通篇所描述的各种功能的电路的任意组合。
其中，处理器602负责管理总线和一般处理(包括执行存储在存储介质1203上的软件)。处理器602可以使用一个或多个通用处理器和/或专用处理器来实现。处理器的例子包括微处理器、微控制器、DSP处理器和能够执行软件的其它电路。应当将软件广义地解释为表示指令、数据或其任意组合，而不论是将其称作为软件、固件、中间件、微代码、硬件描述语言还是其它。
在下图中存储介质603被示为与处理器602分离，然而，本领域技术人员很容易明 白，存储介质603或其任意部分可位于通信装置600之外。举例来说，存储介质603可以包括传输线、用数据调制的载波波形、和/或与无线节点分离开的计算机制品，这些介质均可以由处理器602通过总线接口604来访问。可替换地，存储介质603或其任意部分可以集成到处理器602中，例如，可以是高速缓存和/或通用寄存器。
处理器602可执行上述实施例中，例如，图3a、图3b、图3c、图3d、图4a和图4b依次对应的上述实施例一、实施例二、实施例三、实施例四、实施例五和实施例六，在此不再对处理器602的执行过程进行赘述。
本申请实施例所说的通信装置，可以是接入点、站点、基站或者用户终端等无线通信设备。
本申请实施例所说的的Polar码，包括但不限于Arikan Polar码，还可以是CA-Polar码或者PC-Polar码。Arikan Polar是指原始的Polar码，没有与其它码级联，只有信息比特和冻结比特。CA-Polar码是Polar码级联了循环冗余校验(Cyclic Redundancy Check，简称CRC)的Polar码，PC-Polar码是Polar码级联了奇偶校验(Parity Check，简称PC)的码。PC-Polar和CA-Polar是通过级联不同的码来提高Polar码的性能。
本申请实施例所说的“信息比特序列”，也可以叫做“待编码比特序列”或者“信息比特集合”，相应的，“信息比特个数”可以是待编码比特序列中待编码比特的个数，或者信息比特集合中的元素个数。
本申请实施例描述的各示例的单元及方法过程，能够以电子硬件、或者计算机软件和电子硬件的结合来实现。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能。
在本申请所提供的几个实施例中，应该理解到，所揭露的装置和方法，可以通过其它的方式实现。例如，以上所描述的装置实施例仅仅是示意性的，例如，所述单元的划分，仅仅为一种逻辑功能划分，实际实现时可以有另外的划分方式。例如多个单元或组件可以结合或者可以集成到另一个系统，或一些步骤可以忽略，或不执行。此外，各个单元相互之间的耦合或直接耦合或通信连接可以是通过一些接口实现，这些可以是电性、机械或其它的形式。
所述作为分离部件说明的单元可以是或者也可以不是物理上分开的，既可以位于一个地方，也可以分布到多个网络单元上。
另外，在本申请各个实施例中的各功能单元可以集成在一个处理单元中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个单元中。
在上述实施例中，可以全部或部分地通过软件、硬件、固件或者其任意组合来实现。当使用软件实现时，可以全部或部分地以计算机程序产品的形式实现。所述计算机程序产品包括一个或多个计算机指令。在计算机上加载和执行所述计算机程序指令时，全部或部分地产生按照本发明实施例所述的流程或功能。所述计算机可以是通用计算机、专用计算机、计算机网络、或者其他可编程装置。所述计算机指令可以存储在计算机可读存储介质中，或者从一个计算机可读存储介质向另一个计算机可读存储介质传输，例如， 所述计算机指令可以从一个网站站点、计算机、服务器或数据中心通过有线(例如同轴电缆、光纤、数字用户线(DSL))或无线(例如红外、无线、微波等)方式向另一个网站站点、计算机、服务器或数据中心进行传输。所述计算机可读存储介质可以是计算机能够存取的任何可用介质或者是包含一个或多个可用介质集成的服务器、数据中心等数据存储设备。所述可用介质可以是磁性介质，(例如，软盘、硬盘、磁带)、光介质(例如，DVD)、或者半导体介质(例如固态硬盘Solid State Disk (SSD))等。
附录：
表1
N＝32
32,31,30,28,24,16,29,27,26,23,22,15,20,14,12,25,8,21,19,13,18,11,10,7,6,4,17,9,5,3,2,1
N＝64
64,63,62,60,56,48,61,32,59,58,55,54,47,52,46,31,44,57,30,40,53,28,51,24,45,50,43,16,42,29,39,27,38,26,23,36,22,49,15,20,41,14,12,37,25,35,8,21,34,19,13,18,11,10,7,6,33,4,17,9,5,3,2,1
N＝128
128,127,126,124,120,112,125,96,123,122,119,64,118,111,116,110,95,108,121,94,104,117,92,63,115,62,88,109,114,60,107,80,106,93,56,103,91,102,48,90,87,61,100,86,59,32,113,79,58,84,55,78,105,54,76,101,47,52,89,99,46,72,85,98,31,44,83,30,57,77,40,82,28,53,75,51,74,24,45,71,50,70,43,16,42,29,97,68,39,27,38,81,26,23,36,73,22,49,15,69,20,14,41,67,12,37,66,25,35,8,21,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1
N＝256
256,255,254,252,248,240,253,224,251,250,247,192,246,239,244,238,128,223,236,249,222,232,245,220,191,243,190,216,237,242,188,235,127,208,234,221,126,184,231,219,124,230,176,218,215,189,228,120,214,187,160,241,207,186,212,112,183,206,233,125,182,204,229,123,96,175,180,217,122,174,227,200,119,213,226,159,172,64,118,211,158,111,185,205,116,168,210,110,156,181,203,95,108,179,202,152,173,199,94,121,178,104,198,171,92,144,117,63,170,157,196,225,167,115,62,88,109,155,166,114,60,209,154,107,80,151,164,106,93,56,201,150,103,177,91,143,102,197,148,48,90,142,169,87,100,61,195,140,86,59,165,32,194,113,79,153,58,84,136,163,55,78,105,149,54,162,76,101,147,47,52,89,141,46,72,99,146,139,85,44,31,98,138,83,30,57,135,77,40,82,193,28,53,134,75,51,161,74,132,24,45,71,50,70,43,145,16,42,29,68,39,97,137,27,38,81,26,133,23,36,22,73,131,49,15,20,69,130,14,41,67,12,37,66,25,35,8,21,34,19,129,13,18,11,65,10,7, 6,33,4,17,9,5,3,2,1
N＝512
512,511,510,508,504,496,509,480,507,506,503,448,502,495,500,494,384,479,492,505,478,488,501,256,476,447,499,446,472,493,498,444,383,491,464,490,477,382,440,487,475,486,380,432,255,474,471,484,445,376,254,470,443,416,497,463,252,442,468,368,439,462,489,381,438,248,460,379,485,352,431,436,473,378,430,483,456,240,375,469,253,482,415,428,320,374,467,414,367,441,251,224,372,461,424,466,366,250,412,437,459,247,351,364,435,458,192,246,408,429,455,350,377,434,239,360,244,454,427,348,400,373,238,319,426,413,128,452,481,423,371,318,236,223,344,365,411,422,370,222,316,249,465,410,363,232,336,407,420,220,245,362,349,191,312,457,406,359,433,243,347,190,399,358,216,453,404,237,304,346,242,398,188,425,343,356,317,235,127,451,208,396,342,315,234,421,288,221,126,184,450,231,369,335,409,314,340,219,392,419,311,230,334,124,361,176,405,218,310,418,215,228,332,189,120,357,303,403,214,308,187,345,397,160,302,328,355,402,241,207,186,212,112,395,341,183,300,206,287,354,233,125,394,182,339,286,313,204,391,333,296,123,229,96,175,338,180,284,309,390,217,449,122,331,174,200,227,119,307,213,330,280,388,172,159,226,118,64,301,327,417,306,211,158,111,185,326,299,116,205,168,272,401,210,110,156,298,181,285,203,324,295,353,108,95,393,179,283,202,152,294,173,199,94,121,178,282,104,337,198,279,171,292,389,92,144,117,63,278,170,157,329,196,387,167,62,115,88,225,271,305,109,155,276,166,114,325,386,60,270,154,107,209,80,297,151,164,323,106,268,93,56,150,103,201,293,322,91,143,102,281,177,148,264,291,197,48,90,142,87,100,277,61,169,290,195,140,86,59,32,275,165,194,79,113,269,84,58,153,136,274,55,163,78,267,105,149,54,162,385,76,266,101,147,47,52,263,89,141,46,72,99,146,262,321,139,85,44,98,31,289,138,260,83,30,57,40,77,135,82,28,53,134,193,75,273,51,74,132,24,161,45,71,265,50,43,70,16,145,42,261,29,68,39,97,137,27,259,38,81,26,133,258,23,36,22,73,131,15,49,20,69,130,14,41,67,12,37,66,25,257,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1
N＝1024
1024,1023,1022,1020,1016,1008,1021,992,1019,1018,1015,960,1014,1007,1012,1006,896,991,1004,1017,990,1000,1013,768,988,959,1011,958,984,1005,1010,956,895,1003,976,512,1002,989,894,952,999,987,892,998,944,767,986,983,957,996,888,766,982,955,928,1009,975,764,954,980,880,951,974,1001,893,511,950,760,972,891,997,864,510,943,948,985,890,942,995,968,752,887,508,981,765,994,927,940,832,886,979,504,926,879,953,763,736,884,973,936,978,878,762,924,949,971,759,496,863,876,947,970,704,758,920,509,941,967,862,889,946,751,872,507,756,966,939,480,860,912,885,750,831,506,938,925,640,964,993,935,503,883,830 ,748,856,735,877,923,934,448,882,502,734,828,761,977,922,875,744,495,848,919,932,500,732,874,757,861,703,824,494,918,969,871,755,859,702,945,384,911,870,728,916,965,492,479,749,816,858,754,910,700,855,937,868,829,478,747,639,505,963,720,488,908,854,827,746,933,800,733,638,696,476,962,501,743,881,847,447,256,921,852,826,731,904,931,823,742,846,636,446,499,472,873,688,730,917,493,822,930,727,498,740,844,701,444,632,869,815,915,491,383,726,820,464,699,857,909,672,814,840,867,914,490,719,753,477,382,440,724,698,487,624,907,853,695,812,718,799,866,475,745,637,486,380,906,694,851,798,825,432,716,474,903,255,845,808,635,741,608,687,471,484,850,445,692,796,376,821,902,729,634,686,254,843,961,712,470,739,631,443,416,819,725,842,463,497,792,684,900,671,738,630,252,468,576,442,813,839,368,929,818,439,462,723,670,623,697,489,381,838,811,628,680,717,438,784,248,722,622,460,913,668,810,693,379,797,485,431,352,715,836,807,436,865,620,473,607,378,691,430,905,456,795,664,483,714,806,240,375,685,606,711,633,690,469,794,428,616,415,253,374,482,849,320,710,791,683,804,901,604,656,467,629,414,575,367,251,441,224,372,790,682,424,461,669,841,708,679,366,466,574,899,627,412,600,250,737,783,437,817,621,667,459,788,247,678,837,626,898,364,351,572,782,435,666,458,619,408,246,721,192,809,592,663,429,350,676,455,835,377,434,618,360,780,239,605,568,662,244,615,454,427,713,805,348,400,834,373,238,319,603,655,689,793,614,426,413,660,776,452,709,803,128,423,318,560,371,602,344,236,654,223,481,599,365,411,612,789,573,681,422,370,802,707,222,316,652,598,249,410,363,465,232,571,787,544,336,677,407,420,706,591,625,220,362,781,596,245,570,312,349,191,665,406,359,648,786,457,567,590,675,347,190,243,779,617,399,433,358,216,661,566,404,674,237,453,304,588,897,346,242,398,778,188,343,559,356,613,659,317,564,425,235,775,127,208,451,601,653,558,396,342,584,611,658,315,234,288,221,126,184,421,774,833,450,231,335,369,651,597,556,409,340,314,543,610,219,392,311,230,334,124,419,650,542,772,595,176,361,218,569,405,310,647,801,552,589,418,215,228,332,189,594,120,540,357,303,403,565,646,705,214,308,187,160,587,345,302,397,328,785,207,355,402,563,241,586,536,212,186,644,112,395,557,341,583,183,300,206,287,673,354,562,777,233,125,394,182,582,555,339,286,313,204,528,296,391,123,333,175,96,229,657,554,180,338,284,541,773,580,309,390,217,551,122,174,331,200,449,609,227,119,539,649,771,307,550,213,330,280,388,172,159,64,118,226,301,327,538,306,417,593,158,211,535,111,548,645,185,116,326,299,770,168,205,272,210,110,534,401,585,156,298,181,643,285,203,324,295,561,353,527,108,95,179,532,152,202,283,294,581,393,526,173,94,642,199,121,178,282,104,553,337,579,198,279,171,389,292,92,524,144,117,63,278,170,549,157,329,196,578,167,62,115,387,88,225,537,271,305,520,109,155,276,166,547,114,325,60,270,386,154,107,533,209,297,80,546,151,164,323,106,268,56,93,150,531,103,201,293,322,525,91,769,143,177,281,102,530,148,264,197,291,48,90,142,523 ,87,100,277,61,169,290,195,641,522,140,86,59,275,165,32,519,79,194,113,269,84,58,153,136,274,55,163,518,78,577,267,105,149,54,162,385,47,76,266,101,147,52,516,263,545,89,141,46,72,99,146,262,321,529,521,289,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1
N＝2048
2048,2047,2046,2044,2040,2032,2045,2016,2043,2042,2039,2038,1984,2031,2036,2030,1920,2028,2015,2014,2041,2024,2012,2037,1983,1792,2035,1982,2008,2029,2034,1980,2027,1919,2000,1536,2026,2013,1918,1976,2023,2011,2022,1916,1968,2010,1791,2007,2020,1981,1912,1790,1024,2006,1979,1952,2033,1999,1788,1978,2004,1904,1975,1998,2025,1917,1535,1974,1784,1996,1915,2021,1888,1967,1534,1972,2009,1914,1966,1992,2019,1776,1911,1532,2005,1789,1964,1951,2018,1910,1856,2003,1023,1950,1528,1903,1787,1977,1760,1908,1960,1997,2002,1902,1948,1786,1022,1973,1995,1783,1520,1900,1887,1971,1994,1020,1944,1782,1728,1533,1965,1991,1886,1913,1970,1775,1896,1780,1531,1990,1963,1504,1884,1936,1016,1909,1774,1855,1962,1530,1949,1988,1664,1959,1907,1527,1854,2017,1880,1772,1759,1901,1947,1958,1008,1906,1526,1472,1758,1852,1785,1946,1899,2001,1768,1021,1872,1519,1943,1956,1524,1756,1898,1781,1885,1848,1727,1942,1518,1019,1895,1993,992,1883,1779,1726,1969,1408,1935,1894,1752,1018,1940,1516,1503,1773,1989,1840,1015,1882,1778,1934,1724,1879,1892,1961,1853,1502,1771,1663,1014,1529,960,1987,1744,1512,1932,1878,1851,1770,1824,1757,1662,1720,1957,1007,1500,1767,1986,1871,1525,1012,1471,1905,1280,1876,1850,1945,1755,1928,1006,1847,1766,1870,1955,1660,1470,1523,1496,1712,1897,1754,1941,896,1846,1517,1954,1004,1751,1868,1764,991,1522,1725,1468,1656,1839,1893,1939,1515,1750,1844,1407,990,1488,1723,1881,1696,1933,1017,1838,1864,1000,1891,1514,1743,1938,1777,1501,1464,1406,1748,1722,1511,1648,988,1931,1877,1719,1836,1742,1013,1823,959,1890,768,1499,1661,1769,1510,1404,1718,1930,1875,1822,958,1011,1456,1740,1849,1498,984,1927,1832,1869,1659,1279,1711,1632,1765,1495,1005,1508,1874,1716,1469,1820,1010,1400,1845,1926,1753,956,1658,1710,1278,1867,1736,1494,1985,1763,1003,1655,1467,895,1440,976,1843,1866,1749,1487,1816,1708,1521,1695,1924,1654,1762,1492,1276,1600,1466,1002,512,1837,1863,952,1392,989,894,1463,1842,1486,999,1953,1694,1747,1647,1721,1405,1652,1862,1835,1513,1704,987,1741,1462,1808,998,892,1272,1646,1746,1484,1692,1937,1834,944,1717,1403,986,1455,1376,1821,1509,1739,1860,767,1460,1831,983,996,1644,1631,957,1889,1497,1402,1454,1715,1480,888,1738,1688,1819,1507,1830,1264,1399,1929,766,982,1709,1630,1735,955,1657,1714,1493,928,1818,1452,1640,1439,127 7,1398,1506,1344,1873,975,1734,1815,1707,1828,1009,1925,1628,980,764,954,1680,1438,1491,1653,880,1599,1391,1275,951,1465,974,1396,1248,1814,1706,1448,1485,1693,1865,1732,893,1703,1001,1390,1490,1598,1923,1651,1436,1624,950,511,1274,1807,1761,1461,760,972,1645,1691,1483,1841,1812,1271,1702,1650,891,1861,1388,943,864,1375,1596,997,510,1922,1806,948,1459,1690,1482,1432,1643,1270,1216,1745,1616,1833,985,890,942,1687,1374,1453,1700,1479,968,1859,995,1458,1401,752,887,1642,1384,1804,1263,508,1592,1629,1686,1268,1639,1478,1451,981,1737,1372,940,1829,1424,927,886,765,994,1262,832,1397,1858,1343,1627,1679,1638,1450,1817,1713,1684,1437,1800,926,979,1476,879,504,1152,1447,1584,1342,1827,1733,763,1395,1626,953,1368,884,1260,736,1678,936,1247,973,1505,1623,1435,1389,1636,878,1597,978,1446,1813,924,1705,1394,762,1246,1340,1826,1731,949,1676,1622,971,1434,759,1273,1387,1256,1595,1489,1360,496,1568,876,1811,1431,863,1444,1701,947,1730,1615,1244,970,920,1386,758,1649,704,1620,1336,1594,1805,1373,1269,1215,509,1430,1689,862,941,967,1383,1672,1810,1591,1614,1481,946,1699,889,872,751,1371,1214,1267,1423,756,1803,1641,1240,1382,966,939,507,1457,1685,1590,860,1428,480,912,1261,750,1328,1698,1612,885,831,1477,1370,1422,1266,938,1802,1212,1583,506,1367,925,1380,1637,1921,1683,964,1341,1588,1259,1449,640,935,830,883,1151,503,1799,1232,856,748,1475,735,1582,1625,1420,1366,1677,1608,993,923,877,1339,1258,1635,934,1682,1312,1208,1245,1150,882,502,448,1445,1798,734,828,1255,1359,1474,1675,922,1621,761,1393,1580,875,1364,1857,744,1338,848,1567,1433,1634,1243,1416,977,919,495,932,1335,1254,1358,1148,1443,500,732,874,1674,1566,1619,824,1200,1796,861,757,703,1242,918,1385,494,1334,871,1593,1429,1576,1671,969,1239,1613,1356,1252,1442,1825,1213,859,702,1618,755,911,1144,1564,728,870,1327,384,1381,916,945,1427,1332,1238,1670,1589,492,479,749,1611,816,1211,858,965,1184,910,754,1326,1369,1421,1729,1352,700,855,1231,868,1379,1426,1809,478,829,1236,747,1560,1210,1587,1610,1265,937,639,720,1136,1668,505,488,963,1207,908,854,1324,1230,1419,1581,1365,1607,1311,1378,746,827,1586,800,696,638,733,476,1697,1149,933,1257,743,1206,847,1310,1418,501,962,1606,447,1579,1363,852,1228,1801,826,256,881,1552,1337,1320,921,904,731,1415,1147,1357,823,742,1199,846,1120,636,931,1253,446,1204,1578,1362,499,472,1308,688,1565,1681,730,1604,873,1414,822,1198,1146,1333,1575,1224,1241,917,1797,493,1355,727,844,740,930,1143,1251,498,701,444,1473,632,1563,1633,815,1574,1331,1304,869,1354,1196,820,726,491,1237,915,1183,1142,1673,383,1412,464,1088,1250,699,1795,672,1325,1351,814,1562,857,840,909,1330,719,1182,490,867,914,1135,440,1235,1559,724,382,477,1441,1572,698,1617,753,1140,1192,624,487,1350,1209,1323,812,695,1296,1229,718,1669,907,853,799,1134,1794,1234,866,1180,1558,475,486,637,1322,380,694,1205,745,798,1309,1227,906,1609,1425,1348,851,716,432,1319,1132,474,1667,808,1551,825,1119,903,635,687,845,255,1556,608,1203,471,1176,484,1226,130 7,692,741,1585,796,850,445,1377,1318,376,1118,1550,1197,1605,1223,1417,686,902,634,821,712,729,254,470,843,1666,1202,1128,1145,1306,631,739,443,416,961,1577,1222,1303,1195,1361,1316,1116,819,792,1168,463,684,842,1603,725,1548,671,1413,630,468,900,1141,442,252,576,1087,738,497,813,368,839,1302,1194,439,462,818,1181,670,1573,1220,723,623,929,1191,1353,1086,1139,1112,1602,628,680,697,838,811,381,1411,489,438,1295,717,784,1561,1544,1249,1179,1133,1793,248,913,352,379,460,622,1329,431,1410,668,485,1571,865,722,436,693,1084,1349,378,473,607,1138,240,797,1233,1300,430,620,1557,715,810,1190,375,905,456,1570,1665,836,1104,483,1294,807,1131,664,1321,1178,691,606,1347,253,320,415,633,1080,714,795,1175,374,428,469,1555,685,1188,849,1117,482,616,711,806,1130,901,1225,1292,1549,690,367,1346,224,1127,414,604,1317,251,794,1174,441,575,1554,656,1201,372,467,629,683,710,791,1115,424,1305,737,804,1072,899,1167,366,461,1547,1126,841,1221,1288,250,1601,412,574,1315,669,1172,466,600,682,247,790,1114,437,627,708,817,1085,898,1166,351,679,1546,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,572,837,667,246,408,626,721,788,1056,435,350,678,1083,1110,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,809,1189,360,666,455,1569,835,1103,244,1293,434,568,663,1082,1177,348,676,605,1108,238,319,1298,400,618,1079,713,780,1160,373,427,454,1540,1187,834,1102,481,615,805,1129,662,1291,689,128,1345,223,318,413,603,1078,236,793,1173,344,426,560,1553,655,1186,371,452,614,709,776,1100,423,1290,803,1071,660,365,222,1125,602,1287,249,316,411,573,1076,654,1171,370,465,599,681,232,789,1113,422,612,707,802,1070,897,1165,336,1545,1096,363,1286,220,1123,410,544,1313,191,1170,571,598,652,245,312,407,625,706,787,1055,420,349,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,570,359,665,216,406,596,243,786,1054,433,567,648,1081,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,833,1101,242,404,566,661,1052,346,674,127,1106,208,317,398,588,1077,235,778,1158,343,425,559,1538,1185,356,451,613,775,1099,184,1289,564,659,126,221,288,601,1048,234,315,342,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,801,1069,658,335,1095,124,1285,219,314,409,543,1074,176,1169,340,556,597,651,230,311,392,610,705,772,1040,419,334,1067,1094,361,218,1121,542,1283,189,569,120,650,215,310,405,595,228,785,1053,418,552,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,594,241,308,403,565,646,1051,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,355,212,402,536,183,1050,563,644,125,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,562,657,96,286,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,1093,122,217,284,541,1044,174,338,554,119,649,200,309,390,580,227,770,1038,417,551,1065,331,1091,64,1281,159,539,118,172,213,280,593,226,307,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,116,211,306,401,535,168,1049,548,64 3,110,205,272,585,1032,299,326,156,1059,353,210,534,181,561,642,95,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,106,201,268,525,1028,322,103,293,150,530,177,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1
表2
M＝48,N＝64
48,32,47,46,31,44,30,40,28,45,24,43,42,39,29,16,38,27,36,26,23,22,41,20,15,37,14,25,35,12,34,21,8,19,18,13,11,10,7,33,6,4,17,9,5,3,2,1,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49
M＝72,N＝128
64,63,62,60,56,48,61,72,71,32,59,70,58,55,68,54,47,52,46,31,44,57,30,40,53,28,69,51,24,45,67,50,43,16,66,29,42,39,27,38,26,36,23,49,22,15,20,41,14,65,37,12,25,35,8,21,34,19,13,18,11,10,7,33,6,4,17,9,5,3,2,1,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73
M＝96,N＝128
96,64,95,94,92,63,62,88,80,60,93,56,91,90,48,87,61,86,79,59,84,78,58,32,55,76,54,89,47,72,52,85,46,83,44,77,57,82,31,40,75,53,30,74,51,71,28,45,50,70,24,43,68,42,16,81,39,29,38,27,73,36,26,23,49,69,22,67,41,15,20,14,66,37,12,35,25,8,34,21,19,13,18,65,11,10,7,33,6,4,17,9,5,3,2,1,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97
M＝120,N＝128
120,112,96,119,64,118,111,116,110,108,95,94,117,104,92,115,63,109,114,6 2,88,107,60,106,80,93,103,56,91,102,90,48,61,100,87,113,86,59,32,79,58,84,105,55,78,54,101,76,89,47,52,99,46,72,85,98,31,44,83,57,30,77,82,40,53,28,75,51,74,24,45,71,50,70,43,16,97,42,29,68,39,27,81,38,26,23,36,73,22,49,69,15,20,41,14,67,12,37,66,25,35,8,21,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,128,127,126,125,124,123,122,121
M＝144,N＝256
128,127,126,124,120,112,125,144,143,96,123,142,122,119,64,140,118,111,116,136,110,95,108,121,94,104,63,117,92,141,62,115,88,109,139,114,60,107,80,138,56,93,106,135,103,91,134,48,102,90,61,100,87,132,113,32,86,59,79,58,84,105,55,78,137,54,101,76,47,89,52,99,72,46,133,85,98,31,44,57,83,30,131,77,40,82,53,28,130,75,51,24,74,71,45,50,97,70,16,43,68,29,42,81,39,27,38,26,73,36,23,49,129,22,69,15,20,41,67,14,66,12,37,25,8,35,34,21,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145
M＝160,N＝256
128,127,126,124,120,160,159,158,156,112,125,152,96,123,144,122,119,157,64,118,155,111,116,154,110,151,95,108,121,150,94,104,143,117,148,92,63,142,115,62,109,88,140,114,153,60,107,80,136,106,93,56,149,103,91,102,48,147,90,141,100,61,87,146,113,86,139,59,32,79,105,84,58,138,55,78,135,101,54,76,134,47,89,99,52,72,46,132,98,85,145,44,31,83,57,77,30,40,82,137,53,75,28,51,74,133,24,71,45,50,97,70,131,43,16,68,42,130,29,39,81,27,38,73,26,36,23,49,69,22,15,41,20,67,14,66,37,129,12,25,35,8,34,21,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161
M＝180,N＝256
128,127,126,124,176,160,175,180,174,120,179,172,159,112,125,178,158,168,96,123,156,122,119,173,152,118,64,171,111,116,110,170,157,144,167,95,108,1 21,177,166,155,94,104,117,154,92,164,151,63,115,88,150,109,114,62,169,143,107,148,80,60,93,106,142,165,103,56,91,140,102,153,163,90,48,87,100,136,149,162,61,113,86,32,79,59,147,84,105,141,78,58,146,55,101,76,139,54,89,99,47,138,72,52,135,85,98,46,161,134,31,83,44,77,57,30,82,132,40,145,75,53,28,74,51,71,24,45,137,50,70,97,43,16,133,68,29,42,81,39,131,27,38,73,26,130,23,36,49,69,22,15,67,20,41,14,66,37,12,25,35,8,21,129,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181
M＝192,N＝256
192,128,191,190,188,127,184,126,176,124,189,160,187,120,186,183,112,182,125,175,96,180,123,174,122,159,119,172,185,158,118,168,111,181,156,116,64,110,179,152,173,95,108,178,121,171,94,144,104,157,170,117,92,167,155,115,166,88,109,63,154,114,151,164,62,107,80,177,150,93,106,60,143,103,148,169,91,142,102,56,90,165,87,140,100,48,153,113,86,61,163,136,79,149,32,84,59,162,105,78,58,147,55,101,141,76,146,89,54,99,139,72,47,85,52,98,138,46,135,83,31,44,77,134,57,82,161,30,75,40,132,53,28,74,145,71,51,24,45,70,50,97,137,43,16,68,29,42,133,81,39,27,38,131,73,26,23,36,130,69,49,22,15,67,20,41,14,66,37,12,25,35,8,21,34,129,19,13,18,65,11,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193
M＝240,N＝256
240,224,192,239,238,128,223,236,232,222,220,191,237,216,190,235,188,234,127,231,221,208,184,230,126,219,218,228,124,215,176,189,214,120,187,212,233,160,207,186,183,112,206,125,229,182,204,217,123,227,180,175,96,122,226,200,213,174,119,211,118,159,172,64,185,158,210,205,111,116,168,181,110,203,156,179,202,95,108,152,199,173,178,121,94,198,104,171,225,117,92,144,63,170,157,196,115,167,62,88,209,109,155,166,114,60,154,107,151,164,80,201,106,93,56,150,103,177,197,91,143,102,148,169,48,90,142,195,87,100,61,165,140,86,194,113,59,32,153,79,163,58,84,136,55,78,105,149,162,54,76,101,147,47,52,89,141,99,146,46,72,139,85,98,31,44,138,83,57,30,135,77,193,40,82,53,134,28,75,161,51,74,132,24,45,71,50,145,70,43,16,97,42,29,68,39,137,27,38,81,133,26,23,36,73,131,22,49,69,130,15,20,41,14,67,12,66,37,25,8,35,21,34,129,19,13,18, 11,65,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241
M＝288,N＝512
256,255,254,252,248,240,253,288,287,224,251,286,250,247,192,284,246,239,244,128,280,238,223,236,249,272,222,232,191,245,220,285,190,243,216,237,283,242,188,127,208,235,282,126,184,279,221,234,231,124,278,219,176,230,271,218,120,189,228,215,276,241,160,187,214,270,112,207,186,212,233,125,183,206,268,96,281,182,229,123,204,175,217,264,180,227,122,200,174,119,64,277,213,226,159,172,118,185,211,111,275,158,205,116,168,269,210,110,181,156,274,203,95,108,267,179,152,202,121,94,173,199,178,104,266,225,198,144,63,171,92,117,263,196,170,157,62,115,88,167,209,262,109,155,60,114,166,80,260,107,154,201,164,151,56,273,106,93,177,103,150,197,48,143,91,102,148,169,195,142,265,90,61,100,87,194,32,165,113,140,59,86,153,261,79,163,136,58,84,105,55,78,162,149,259,54,101,76,147,47,258,89,141,52,146,99,72,46,193,139,98,85,31,44,138,30,57,135,83,40,77,161,82,134,28,53,75,132,24,51,74,145,71,45,16,50,97,257,70,43,137,68,29,42,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385,384,383,382,381,380,379,378,377,376,375,374,373,372,371,370,369,368,367,366,365,364,363,362,361,360,359,358,357,356,355,354,353,352,351,350,349,348,347,346,345,344,343,342,341,340,339,338,337,336,335,334,333,332,331,330,329,328,327,326,325,324,323,322,321,320,319,318,317,316,315,314,313,312,311,310,309,308,307,306,305,304,303,302,301,300,299,298,297,296,295,294,293,292,291,290,289
M＝300,N＝512
256,255,254,252,248,240,288,300,296,253,224,251,250,287,247,192,246,286,239,299,244,128,238,284,223,298,236,249,222,232,280,295,245,191,220,294,190,243,216,237,242,272,188,127,285,235,208,126,184,221,234,292,231,283,124,219,176,230,282,297,218,189,120,228,215,279,241,160,214,187,278,112,207,212,186,233,293,125,183,206,271,276,96,229,182,204,123,270,175,217,291,180,227,122,200,174,119,213,64,226,281,268,159,290,172,118,211,185,111,158,205,264,116,168,277,210,110,181,156,203,95,275,108,179,202,152,121,199,173,94,269,1 78,104,274,225,198,144,171,92,117,63,196,157,170,267,62,115,209,167,88,109,289,155,266,114,166,60,263,80,201,154,107,164,151,56,93,177,106,262,150,103,197,143,91,48,102,148,260,169,195,273,142,90,61,100,87,194,165,113,32,140,86,59,153,79,163,136,265,84,58,105,55,149,78,162,54,76,101,261,147,47,89,141,52,146,99,72,46,193,259,139,98,85,31,44,138,258,83,135,57,30,77,40,161,82,134,28,53,75,132,24,74,51,145,71,45,50,97,16,70,43,137,68,29,42,81,39,133,257,27,38,131,26,73,23,36,22,49,130,15,69,20,14,41,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385,384,383,382,381,380,379,378,377,376,375,374,373,372,371,370,369,368,367,366,365,364,363,362,361,360,359,358,357,356,355,354,353,352,351,350,349,348,347,346,345,344,343,342,341,340,339,338,337,336,335,334,333,332,331,330,329,328,327,326,325,324,323,322,321,320,319,318,317,316,315,314,313,312,311,310,309,308,307,306,305,304,303,302,301
M＝360,N＝512
256,255,254,252,352,320,351,350,360,248,359,348,240,319,358,253,344,318,224,251,356,316,250,336,247,349,192,246,312,347,239,244,346,238,304,343,317,223,357,236,128,249,342,222,315,232,335,355,245,191,340,220,314,288,334,311,243,190,354,216,237,332,242,310,345,188,235,303,208,308,234,221,184,127,328,341,231,302,219,126,230,339,176,300,313,218,287,333,189,124,228,215,338,241,286,296,160,214,187,331,309,120,207,353,284,186,212,233,330,307,183,206,112,327,301,280,306,182,229,125,204,326,175,217,299,180,227,96,123,272,200,174,324,298,213,226,122,285,337,295,159,119,172,211,185,64,294,283,158,118,205,168,329,210,111,181,282,292,156,116,203,279,305,110,179,325,202,152,278,173,199,95,108,178,271,121,297,323,198,225,171,276,94,144,104,270,157,170,117,322,196,63,92,293,167,209,268,155,115,62,281,166,88,109,291,154,114,201,264,60,151,164,107,290,277,80,177,150,197,106,56,93,143,275,103,148,169,269,91,195,102,142,48,274,90,194,61,165,267,321,100,87,140,153,113,32,86,59,266,163,136,263,79,149,58,162,84,105,289,55,78,262,147,54,101,141,76,260,47,146,89,52,99,273,139,72,46,193,85,98,138,31,44,135,265,57,83,30,161,77,134,40,82,53,28,261,75,132,145,51,74,24,45,71,259,50,97,70,258,16,137,43,29,68,42,39,133,81,27,38,131,26,73,36,23,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,50 9,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385,384,383,382,381,380,379,378,377,376,375,374,373,372,371,370,369,368,367,366,365,364,363,362,361
M＝384,N＝512
384,256,383,382,380,255,376,254,368,381,252,352,379,248,378,375,320,240,374,253,367,372,224,366,251,351,250,364,247,377,350,192,360,246,373,319,348,239,244,318,371,238,344,365,370,316,223,236,363,336,249,222,349,362,312,232,359,128,245,191,220,347,358,304,190,243,346,317,216,343,237,356,242,188,369,288,342,315,235,208,335,314,340,221,234,184,361,311,231,334,127,219,310,230,357,332,176,303,126,218,345,189,308,215,228,355,302,328,124,241,341,160,214,187,354,287,300,207,186,339,313,120,212,233,286,183,333,206,296,338,309,182,112,284,229,331,204,175,125,217,307,180,330,227,280,200,301,174,327,96,123,213,306,226,159,326,299,172,122,353,272,211,185,119,158,64,205,285,298,324,168,210,118,295,181,156,337,203,283,111,294,116,179,202,282,110,152,173,199,329,279,292,178,95,108,305,198,171,278,225,121,144,94,325,271,157,170,104,196,276,167,297,117,63,92,323,270,209,155,166,62,115,293,322,88,154,109,268,201,151,114,164,281,60,291,107,177,80,150,264,197,277,93,56,106,143,290,103,148,169,195,91,142,275,102,48,269,165,90,194,61,140,274,87,100,153,267,113,32,163,86,59,136,321,79,149,266,162,58,84,105,263,55,78,147,262,54,141,289,101,76,146,47,89,52,139,99,260,72,46,193,85,273,138,98,31,135,44,57,83,30,77,134,161,265,40,82,53,28,75,132,261,145,51,74,24,45,71,50,259,137,97,70,16,43,258,29,42,68,133,39,81,27,38,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385
M＝400,N＝512
384,256,383,382,380,255,376,254,400,368,252,381,399,352,379,248,378,398 ,375,320,240,374,253,396,367,372,224,251,366,351,250,392,364,247,377,350,192,360,246,373,319,348,239,244,371,397,318,238,344,365,370,223,316,236,395,363,249,336,222,349,362,128,312,232,359,394,245,191,220,347,391,358,243,304,190,346,216,237,317,343,356,242,390,188,369,342,235,315,288,208,335,388,234,221,314,340,184,361,231,311,334,127,219,230,310,357,126,176,332,218,303,345,189,215,228,308,355,124,393,328,302,241,214,187,341,160,354,287,207,120,300,186,212,339,233,313,183,389,206,286,333,338,296,112,182,309,229,204,284,125,331,387,175,217,180,307,227,330,96,123,200,174,280,301,327,213,306,386,226,122,159,172,119,326,299,211,185,353,272,64,158,205,118,298,285,168,210,324,295,181,111,156,203,337,116,283,294,110,179,202,152,282,173,199,95,329,178,279,292,108,121,198,171,305,94,225,278,144,104,325,157,170,117,271,196,63,92,167,276,297,209,323,155,270,115,62,166,385,88,109,154,293,114,322,268,201,151,60,164,107,281,80,177,291,150,93,106,264,197,56,103,143,277,290,148,169,91,195,102,142,48,275,90,61,165,269,87,194,100,140,274,153,113,86,32,59,163,267,136,79,149,58,84,321,162,105,266,55,78,263,147,54,101,141,76,262,289,47,146,89,52,99,139,72,46,260,85,193,98,138,31,273,44,135,83,57,30,77,134,40,82,161,53,265,28,75,132,51,74,145,24,261,45,71,50,70,43,259,97,16,137,29,42,258,68,39,133,81,27,38,131,26,73,36,23,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401
M＝480,N＝512
480,448,384,479,478,476,447,256,472,446,464,444,477,383,440,475,382,474,432,471,380,445,470,255,463,376,443,468,254,462,442,439,416,368,252,460,381,438,473,431,379,456,436,248,469,430,352,378,375,467,240,428,461,374,253,441,415,466,320,367,424,459,372,251,414,437,366,224,458,250,412,435,455,247,364,429,351,434,454,246,408,377,192,427,360,350,239,244,373,452,426,400,238,348,423,319,413,371,465,422,365,128,236,318,344,411,223,370,249,363,420,457,410,316,222,232,407,336,362,245,433,359,349,220,453,406,312,191,243,358,399,347,190,425,404,237,451,216,242,398,304,346,356,343,235,188,317,450,421,127,396,208,342,369,234,315,221,419,231,409,288,126,184,335,340,314,392,361,219,230,311,334,418,405,124,176,218,310,357,228,332,215,189,403,303,120,397,345,308,214,355,241,187,402,302,328,160,207,395,354,341,212,186,112,233,300,183,206,287,394,125,339,449,313,391,182,286,333,204,229,296,123,338,175, 96,390,309,180,217,284,331,227,122,174,200,417,119,307,388,330,213,226,280,301,327,172,159,118,64,306,211,185,326,111,158,299,401,205,116,168,272,210,110,353,298,181,156,285,324,203,295,393,108,179,95,202,283,294,152,173,199,337,121,389,94,178,282,104,198,292,279,171,117,329,144,92,387,63,225,170,278,157,196,305,167,115,62,271,325,88,386,109,155,276,166,114,209,270,297,60,107,154,323,80,151,164,268,106,201,93,293,56,322,150,103,177,281,91,143,102,291,197,264,148,48,90,142,277,169,290,87,100,61,195,275,140,86,165,194,59,32,113,269,79,153,274,58,84,163,136,55,78,267,105,385,149,162,54,266,76,101,147,47,263,52,321,89,141,99,46,72,146,262,139,85,98,31,44,289,260,138,83,57,30,135,77,40,193,82,273,53,134,28,75,51,74,132,24,161,45,71,265,50,70,43,145,261,16,97,42,29,68,137,39,27,259,38,81,26,133,258,23,36,73,131,22,49,69,15,130,20,41,14,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481
M＝576,N＝1024
512,511,510,508,504,496,509,576,575,480,507,574,506,503,448,572,502,495,500,384,568,494,479,492,560,505,478,256,488,447,501,476,573,446,499,544,472,493,571,498,444,383,464,491,570,382,440,477,567,490,487,380,566,475,432,255,486,559,474,376,445,254,484,471,564,416,497,558,470,443,252,368,463,543,442,468,489,381,439,462,556,248,352,569,438,485,542,460,379,431,473,240,552,436,378,483,456,430,375,540,565,320,253,469,482,415,224,374,428,251,467,441,367,563,414,536,461,372,424,557,466,250,366,412,437,562,247,192,459,351,528,364,555,246,408,435,458,377,350,455,429,239,541,434,360,128,244,554,481,400,454,348,319,427,238,373,551,452,223,413,426,539,318,236,344,371,423,465,550,365,249,222,411,316,370,422,538,232,336,548,535,410,363,457,220,191,420,245,407,312,561,349,433,362,534,190,406,359,453,216,243,399,304,527,347,237,358,404,188,425,242,532,451,127,398,553,346,208,317,356,526,343,235,450,288,126,184,396,421,369,221,234,342,315,409,524,231,549,335,124,419,392,340,176,314,219,361,537,230,311,334,405,418,120,520,218,547,189,310,228,332,215,357,160,403,303,241,345,546,533,397,308,214,112,187,402,328,355,302,207,449,395,212,186,354,341,287,233,531,125,183,206,300,96,394,525,286,339,391,313,182,530,204,123,229,296,333,417,175,338,390,284,217,180,122,523,64,309,200,227,331,174,119,388,280,226,213,330,159,307,401,522,118,172,327,301,519,306,111,158,272,211,353,185,326,116,168,205,299,545,393,110,210,518,156,324,285,298,181,95,203,108,295,337,152,389,516,94,202,283,179,294,121,199,104,173,529,387,282,178,144,329,225,92,292,198,63,279,117,171,386,305,278,62,196,88,157,325,170,271,115,167,209,521,276,60,109,297,323,155,270,114,80,166,322,154,107,56,201,268,164,151,293,517,93,106,177,281,150,264,103,48,197,29 1,143,91,515,102,148,290,385,277,195,142,169,32,90,61,514,100,87,194,275,140,113,165,269,86,59,274,153,79,136,321,163,58,84,267,55,78,105,162,149,266,54,263,76,47,101,147,289,262,52,141,72,89,46,146,99,260,193,31,139,44,98,85,273,30,513,138,40,135,83,57,77,28,82,53,134,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937,936,935,934,933,932,931,930,929,928,927,926,925,924,923,922,921,920,919,918,917,916,915,914,913,912,911,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,839,838,837,836,835,834,833,832,831,830,829,828,827,826,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811,810,809,808,807,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,718,717,716,715,714,713,712,711,710,709,708,707,706,705,704,703,702,701,700,699,698,697,696,695,694,693,692,691,690,689,688,687,686,685,684,683,682,681,680,679,678,677,676,675,674,673,672,671,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,609,608,607,606,605,604,603,602,601,600,599,598,597,596,595,594,593,592,591,590,589,588,587,586,585,584,583,582,581,580,579,578,577
M＝600,N＝1024
512,511,510,508,504,496,576,600,592,509,480,507,506,575,503,448,502,574,495,599,500,384,494,572,598,479,492,505,478,256,488,568,596,501,476,447,591,446,499,472,590,493,560,498,444,383,464,491,573,588,440,382,477,490,487,571,380,544,475,432,255,486,597,570,474,445,376,484,471,254,567,416,497,584,443,470,595,252,368,463,566,442,468,489,439,381,462,559,248,594,589,352,564,438,485,460,379,431,473,558,240,436,483,378,587,456,430,375,320,253,469,55 6,482,415,543,569,428,374,224,586,441,467,251,414,367,461,552,372,424,542,466,250,583,366,437,412,565,192,247,459,351,540,364,435,582,408,458,246,377,563,429,455,350,239,434,593,360,557,481,244,400,454,536,427,580,319,373,348,128,562,238,413,452,426,318,223,555,423,371,465,344,236,365,528,411,249,222,422,316,370,554,585,232,336,410,541,457,363,551,420,407,191,220,245,312,433,349,362,406,550,190,359,453,539,216,243,399,304,347,581,237,404,358,425,188,451,242,548,538,398,346,127,317,208,356,561,343,235,535,450,288,421,396,184,369,579,126,221,315,342,234,409,534,231,335,419,392,578,124,314,340,176,527,361,219,553,311,405,230,418,334,532,218,189,120,526,310,228,357,332,403,215,160,303,549,241,397,345,308,402,187,214,355,524,328,112,302,207,449,395,537,186,212,354,341,547,287,233,183,300,125,206,394,520,96,391,286,313,339,546,182,204,229,296,333,533,123,417,175,338,390,284,217,180,309,122,227,200,331,64,174,388,119,531,280,577,307,226,213,330,401,159,172,525,327,301,118,530,306,158,185,211,353,111,272,326,168,116,299,205,393,523,210,156,110,324,285,298,181,203,95,295,522,337,108,389,152,519,283,179,202,294,94,121,545,199,173,387,104,178,282,329,144,225,292,518,279,198,92,63,171,386,117,305,278,196,157,62,325,170,516,88,271,167,115,209,276,529,60,297,109,155,323,270,166,114,80,154,322,201,268,107,164,56,293,151,521,93,177,281,106,150,264,103,291,197,48,143,91,148,102,290,277,385,169,142,195,517,90,32,61,100,87,194,275,140,165,113,269,59,86,274,515,153,136,79,321,163,58,267,84,514,55,105,162,149,78,266,54,263,76,101,147,47,289,262,52,141,89,72,146,46,99,260,193,31,139,44,98,85,273,30,138,135,40,57,83,28,134,161,77,82,265,513,24,53,132,75,16,261,74,51,145,71,45,50,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937,936,935,934,933,932,931,930,929,928,927,926,925,924,923,922,921,920,919,918,917,916,915,914,913,912,911,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,839,838,837,836,835,834,833,832,831,830,829,828,827,826,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811,810,809,808,807,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,76 1,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,718,717,716,715,714,713,712,711,710,709,708,707,706,705,704,703,702,701,700,699,698,697,696,695,694,693,692,691,690,689,688,687,686,685,684,683,682,681,680,679,678,677,676,675,674,673,672,671,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,609,608,607,606,605,604,603,602,601
M＝720,N＝1024
512,511,510,508,704,640,703,702,720,504,719,700,496,639,718,509,696,480,638,507,716,688,506,636,503,701,448,712,502,632,699,495,672,500,698,494,384,695,624,479,717,492,637,694,505,478,715,488,687,635,692,608,501,447,476,686,714,634,499,446,256,711,631,472,493,671,684,498,697,444,383,630,710,491,464,670,680,623,382,477,490,576,693,440,628,487,668,708,622,475,380,691,486,432,474,607,664,685,620,445,690,471,484,376,633,497,255,606,416,470,683,443,713,616,463,629,368,656,254,682,442,468,669,604,489,381,439,679,462,709,627,575,252,667,438,352,485,600,678,379,621,460,626,431,473,574,707,666,248,436,483,378,676,663,619,456,430,375,689,469,592,572,320,482,706,415,662,618,605,374,240,428,615,467,441,367,568,253,414,655,461,660,603,681,372,424,466,614,366,437,224,412,654,251,459,602,560,351,677,612,599,435,364,250,458,625,573,652,408,377,429,455,247,665,350,598,434,675,192,360,544,454,571,246,481,427,591,648,400,373,319,348,596,661,617,674,239,413,426,570,452,244,590,318,371,423,567,465,344,238,659,128,365,613,705,411,370,422,588,566,223,316,653,601,658,236,410,363,336,457,611,249,559,407,420,222,564,584,651,349,312,362,433,232,597,558,610,406,359,453,245,220,191,650,347,399,543,358,304,595,647,404,556,425,243,451,190,569,346,398,216,589,317,542,237,673,343,356,594,646,242,450,552,421,369,188,288,396,127,342,315,565,587,235,409,208,540,644,335,419,126,314,392,221,184,340,234,586,657,361,563,311,231,405,334,583,536,418,557,219,124,562,310,230,357,609,176,582,403,332,303,649,218,345,555,397,528,189,308,215,228,120,355,402,580,328,302,241,541,554,160,395,341,214,593,187,354,551,449,645,287,112,207,300,394,539,212,186,339,313,233,550,391,286,125,183,206,333,643,585,296,538,338,417,96,390,548,535,309,182,229,284,123,204,331,642,561,217,175,581,388,534,180,307,227,122,330,280,200,401,174,119,301,327,527,213,64,306,226,532,553,159,579,353,118,326,172,272,299,526,211,185,393,111,158,205,578,285,298,116,324,168,549,210,295,524,110,337,181,156,537,203,389,283,95,294,547,108,179,520,202,152,282,121,329,387,199,173,94,533,292,279,546,178,104,305,641,225,198,386,144,171,278,63,117,9 2,325,531,271,157,196,525,170,62,276,297,115,167,88,209,530,323,270,109,155,114,60,166,523,577,322,293,268,80,107,154,201,151,164,281,522,56,93,106,291,177,519,264,150,103,197,277,290,545,143,91,48,102,518,148,169,195,385,90,142,275,61,100,87,516,269,194,32,165,113,140,274,86,59,529,153,267,79,163,321,136,58,84,105,55,266,149,78,162,263,521,54,101,76,147,289,47,262,89,141,52,517,146,99,72,46,260,193,139,85,98,31,273,515,44,138,30,57,83,40,135,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937,936,935,934,933,932,931,930,929,928,927,926,925,924,923,922,921,920,919,918,917,916,915,914,913,912,911,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,839,838,837,836,835,834,833,832,831,830,829,828,827,826,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811,810,809,808,807,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721
M＝768,N＝1024
768,512,767,766,764,760,511,510,752,765,508,736,763,504,762,759,704,496,758,509,751,756,640,750,480,507,735,748,506,761,734,503,744,448,757,703,502,732,495,702,755,500,728,749,494,384,754,700,639,747,479,720,492,638,733,746,505,696,478,743,488,731,636,501,742,447,688,476,730,701,727,632,740,446,499,472,493,753,672,726,699,498,444,719,383,624,491,698,724,464,745,256,695,637,718,382,477,490,440,487,694,741,608,635,716,475,687,380,729,486,692,432,634,739,474,686,712,631,445,471,725,484,376,576,738,671,630,684,497,416,470,443,723,697,623,670,463,717,368,628,680,442,722,468,255,489,622,693,439,381,668,462,715,254,607,438,352,691,620,485,379,714,460,664,633,685,431,711,473,606,252,690,436,378,483,616,456,430,710,683,375,629,737,656,575,604,469,320,482,248,415,669,682,374,428,708,574,627,679,467,441,600,367,414,621,7 21,667,461,240,372,626,678,424,466,572,366,437,253,619,666,412,459,592,713,663,676,351,224,605,618,568,435,364,251,458,689,408,615,662,377,429,455,350,709,434,250,603,655,360,614,247,560,660,454,427,681,481,373,319,400,192,602,348,707,654,573,246,599,612,413,426,452,318,371,423,677,239,706,625,652,544,344,598,571,365,465,244,411,665,370,422,128,238,591,316,675,570,596,363,648,410,617,336,567,223,457,407,661,590,420,236,674,349,362,312,249,433,566,222,359,406,613,588,659,453,232,559,347,399,601,653,358,245,191,304,564,404,220,425,611,658,346,451,584,558,398,317,343,190,356,651,597,243,610,216,543,421,237,450,369,288,396,556,705,342,315,242,650,409,595,188,569,127,542,647,335,235,419,589,208,314,340,392,552,361,594,311,126,405,334,221,234,184,565,646,418,540,673,587,231,310,357,124,219,332,403,563,644,230,586,303,176,345,536,397,557,308,583,218,355,657,402,189,562,328,302,120,215,228,395,341,582,555,609,354,241,528,160,287,214,187,449,300,649,394,112,541,313,339,554,207,580,286,391,186,212,551,333,233,125,183,296,593,206,338,539,390,309,645,417,284,550,331,96,182,229,123,204,538,175,307,217,388,585,330,535,548,643,280,180,122,227,301,327,401,200,174,119,306,561,64,534,213,642,226,326,581,159,299,353,272,118,172,527,211,185,393,532,285,111,298,158,553,324,205,579,116,295,526,168,210,337,110,181,283,156,389,203,294,549,578,524,95,282,108,179,537,202,329,152,387,279,121,292,173,199,94,547,178,520,305,104,278,386,198,533,225,171,325,63,144,117,546,92,271,157,276,170,297,196,62,115,531,323,167,641,270,88,209,109,525,155,114,60,166,293,530,322,268,107,154,80,281,201,523,151,164,56,291,577,93,106,264,177,103,150,522,277,197,290,91,519,143,48,102,148,169,385,275,195,90,545,142,518,87,61,100,269,274,165,194,113,32,140,59,86,516,153,267,79,321,529,163,58,136,84,105,266,55,149,78,162,263,54,521,101,289,76,262,147,47,89,141,52,46,72,99,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937,936,935,934,933,932,931,930,929,928,927,926,925,924,923,922,921,920,919,918,917,916,915,914,913,912,911,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,839,838,837,836,8 35,834,833,832,831,830,829,828,827,826,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811,810,809,808,807,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769
M＝960,N＝1024
960,896,959,768,958,956,895,952,512,894,944,892,957,928,955,767,888,954,766,951,880,950,764,893,943,948,864,891,511,942,760,890,927,940,887,510,953,752,926,886,936,765,508,879,949,924,884,763,736,832,878,947,504,920,941,762,863,876,946,759,889,939,862,496,758,912,872,509,938,925,751,885,860,704,935,756,507,923,750,480,883,934,856,831,877,922,506,735,882,748,919,932,503,830,875,640,761,734,848,918,502,744,874,945,828,861,448,871,911,757,732,495,916,500,859,870,910,824,937,703,494,755,728,858,749,855,702,868,754,908,479,933,492,384,816,747,854,921,829,720,505,478,700,881,931,904,746,847,639,733,488,852,827,743,800,917,501,476,930,846,873,696,638,731,826,742,447,256,823,915,499,730,844,869,472,636,446,909,493,727,740,822,688,498,914,857,701,867,815,726,491,840,907,444,632,820,753,464,853,383,719,699,814,672,866,490,724,477,906,487,718,698,382,440,903,745,851,799,812,624,695,475,845,486,637,902,825,716,798,850,741,694,380,474,808,432,843,471,729,635,484,687,608,255,821,796,929,445,692,739,712,900,842,470,376,634,686,725,254,839,819,631,497,443,738,416,792,463,813,671,468,684,913,723,630,838,818,442,252,576,462,368,489,717,439,670,811,697,623,722,784,381,680,628,865,836,905,438,460,715,810,622,797,485,668,693,248,807,379,352,431,473,714,436,849,795,607,901,691,620,483,456,806,711,378,430,664,685,240,375,469,794,633,606,690,482,710,899,791,841,616,804,253,415,428,683,374,320,467,656,629,604,737,790,441,414,708,461,575,367,682,251,669,224,898,372,424,466,837,817,679,627,783,366,574,600,459,412,788,437,250,667,621,678,721,626,247,782,835,809,458,351,364,666,435,572,619,408,455,663,246,592,676,429,192,780,713,350,834,377,434,618,805,605,239,454,360,662,568,615,427,244,793,689,400,348,373,709,603,655,238,803,776,319,614,426,660,452,413,481,423,371,602,789,654,128,560,318,681,707,344,223,802,236,599,612,411,365,573,422,370,465,787,652,222,249,598,706,316,410,677,363,571,781,544,232,336,407,420,625,591,665,786,457,362,220,596,245,349,570,675,648,897,191,406,359,312,590,779,567,617,433,661,347,243,399,453,674,190,358,216,404,566,778,237,588,346,304,613,398,242,659,775,425,559,451,833,343,188,356,317,601,653,235,564,127,208,658,611,584,396,558,774,342,421,450,234,315,221,288,651,369,597,126,184,231,335,409,610,543,556,340,314,419,392,801,772,219,650,230,334,311,595,124,361,542,569,647,405,176,589,218,418,705,552,310,594,215,332,228,189,357,646,785,540,565,403,120,303,587,214,308,345,397,187,160,355,241,402,328,302,563,673,586,644,207,536,212 ,777,186,395,583,557,341,112,354,183,562,206,287,300,233,125,394,582,555,339,657,182,286,313,391,773,528,204,333,229,449,296,123,96,554,338,175,541,580,180,609,390,284,217,309,551,331,122,649,227,174,200,771,539,119,550,307,213,330,388,417,280,226,593,159,172,327,301,118,64,538,645,770,306,211,535,548,158,111,185,326,299,205,116,168,401,585,272,210,534,643,110,156,181,298,285,203,561,353,324,527,295,581,108,532,95,393,642,179,202,283,152,294,526,173,199,553,94,337,121,178,579,282,389,104,198,279,171,292,524,549,117,144,92,63,329,578,278,170,387,157,196,225,537,167,115,62,305,271,88,547,520,325,109,155,386,276,166,114,533,209,270,154,60,107,297,546,80,323,151,164,531,106,268,769,93,201,56,293,150,103,322,525,177,281,530,91,143,197,102,291,264,148,48,523,90,142,277,169,641,87,100,61,290,195,522,140,86,275,519,165,59,194,32,577,113,269,153,79,274,518,58,84,163,385,136,55,105,267,78,545,149,162,516,54,266,101,321,76,147,263,529,47,89,141,52,99,46,521,72,262,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961
M＝1200,N＝2048
1024,1023,1022,1020,1016,1008,1152,1200,1184,1021,992,1019,1018,1151,1015,960,1014,1150,1199,1007,1012,896,1006,1148,1198,991,1004,1017,990,768,1000,1144,1196,959,1013,988,1183,958,1011,984,1192,1005,512,1136,1010,956,1182,895,976,1003,1149,894,952,989,1002,1180,999,1120,892,1147,987,944,767,998,1197,986,1176,888,957,1146,996,983,766,928,1009,1143,955,982,1195,880,764,975,1142,954,511,980,1088,1001,893,951,974,760,1194,1135,864,510,950,1191,997,1140,891,972,1181,943,985,1168,752,948,1134,890,508,995,968,942,887,832,1190,765,981,1119,1179,994,927,1132,504,886,940,736,1145,953,979,763,879,926,1188,1118,1178,973,884,936,978,1128,496,762,878,1175,924,949,704,759,971,1141,863,1116,509,876,947,920,1174,758,970,889,1087,480,862,941,967,751,1139,946,507,872,1193,1112,756,640,993,912,966,831,939,860,885,1133,750,1172,1086,506,1138,925,448,964,938,1167,830,503,735,883,856,935,748,977,1104,877,1131,1189,1084,761,923,502,828,734,882,934,1166,744,495,848,922,1117,875,969,1130,703,500,384,932,919,732,757,824,1080,1177,1187,1127,861,494,945,874,1164,918,871,702,965,1115,755,479,728,911,816,1126,859,492,1186,749,870,916,937,700,1173,754,505,963,639,1160,478,910,858,1114,1072,829,256,720,868,85 5,488,1124,747,1111,800,962,933,881,638,696,908,447,1085,476,1137,501,827,854,733,746,921,1171,1110,847,743,931,446,1056,636,904,826,852,472,688,873,499,731,1083,823,1103,846,742,917,1170,930,493,1108,1165,444,1129,632,498,383,730,701,822,869,1082,844,740,464,1102,727,915,672,815,491,857,1079,753,909,820,382,440,699,1163,914,726,624,867,840,1125,814,477,490,1100,719,961,1078,907,487,853,698,866,380,799,724,1113,745,637,432,812,1162,695,475,718,906,608,1185,255,1071,486,1123,825,798,851,1159,1096,903,1076,376,694,808,474,845,635,741,716,445,929,850,484,254,687,471,902,1109,796,1122,416,729,1070,821,692,1158,634,497,843,576,739,712,443,686,470,368,631,900,252,1055,792,819,1068,842,463,1107,725,738,913,671,1156,442,813,839,630,468,684,1169,1081,489,381,818,1101,439,1054,462,623,248,784,865,670,697,352,723,1106,838,628,1064,811,680,717,905,438,379,622,722,460,485,668,1052,836,797,1099,810,1077,431,693,240,607,473,715,807,436,849,320,378,620,901,456,483,664,1098,430,795,375,1161,691,714,806,1048,606,633,1075,1095,253,711,685,482,415,469,224,616,794,899,374,690,428,841,804,656,791,737,1069,575,1121,604,710,1074,367,1094,414,683,629,441,817,251,467,898,372,1157,790,1040,424,574,461,837,708,669,682,366,600,192,466,783,1067,412,250,627,1092,679,721,788,437,247,572,351,809,621,459,835,782,667,364,1053,1105,626,1155,1066,678,408,592,246,1063,435,458,350,834,666,377,780,619,568,713,128,805,455,676,239,429,663,360,1154,434,1051,244,605,400,793,618,319,689,481,348,1062,454,776,662,238,615,803,427,373,1097,560,709,1050,655,318,603,223,452,1060,344,413,614,802,660,789,426,1047,236,897,681,371,707,654,423,465,602,573,1073,544,316,222,612,365,1093,599,249,411,787,370,706,1046,422,336,652,232,625,677,781,571,598,191,220,410,786,312,1039,363,457,665,420,407,591,1044,1091,648,245,833,570,675,349,779,596,1065,362,190,433,1038,567,216,617,406,590,359,304,674,453,661,778,1090,243,399,347,566,188,775,358,404,127,588,237,1036,208,613,559,242,425,1061,398,659,451,801,288,317,346,774,564,601,653,356,343,126,184,584,658,235,1153,450,558,1049,611,396,369,421,1032,772,705,315,1059,342,221,543,651,234,610,597,124,409,556,335,785,231,176,392,314,419,650,340,542,1058,1045,311,219,569,647,361,334,595,230,552,120,418,405,589,673,540,218,310,160,189,594,646,777,332,228,215,1043,357,303,565,403,112,587,308,644,536,241,1037,345,397,187,214,328,402,302,1042,355,563,773,586,657,207,1089,449,583,186,287,557,395,96,212,528,354,300,562,125,341,183,1035,206,233,609,771,582,394,286,555,313,391,649,182,339,296,123,770,204,1034,580,64,541,175,333,284,554,229,417,1031,390,338,551,180,122,593,217,200,309,174,645,119,1057,539,280,331,1030,227,388,550,159,118,172,538,307,330,643,226,401,1028,213,548,272,535,327,111,585,301,158,306,116,642,168,534,326,353,185,561,110,211,1041,156,299,527,205,581,393,95,324,532,210,108,285,298,152,526,181,295,94,203,579,769,553,104,337,283,389,1033,144,524,294,63,202,92,578,179,121,282,199,17 3,520,292,387,62,549,178,279,88,198,1029,329,386,537,225,117,278,60,171,80,547,196,157,170,115,305,167,109,271,325,155,114,209,276,533,166,546,641,270,107,297,154,323,56,151,531,164,93,106,201,268,525,322,103,293,150,530,177,91,281,48,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,32,59,86,140,113,194,275,518,165,545,79,269,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,2048,2047,2046,2045,2044,2043,2042,2041,2040,2039,2038,2037,2036,2035,2034,2033,2032,2031,2030,2029,2028,2027,2026,2025,2024,2023,2022,2021,2020,2019,2018,2017,2016,2015,2014,2013,2012,2011,2010,2009,2008,2007,2006,2005,2004,2003,2002,2001,2000,1999,1998,1997,1996,1995,1994,1993,1992,1991,1990,1989,1988,1987,1986,1985,1984,1983,1982,1981,1980,1979,1978,1977,1976,1975,1974,1973,1972,1971,1970,1969,1968,1967,1966,1965,1964,1963,1962,1961,1960,1959,1958,1957,1956,1955,1954,1953,1952,1951,1950,1949,1948,1947,1946,1945,1944,1943,1942,1941,1940,1939,1938,1937,1936,1935,1934,1933,1932,1931,1930,1929,1928,1927,1926,1925,1924,1923,1922,1921,1920,1919,1918,1917,1916,1915,1914,1913,1912,1911,1910,1909,1908,1907,1906,1905,1904,1903,1902,1901,1900,1899,1898,1897,1896,1895,1894,1893,1892,1891,1890,1889,1888,1887,1886,1885,1884,1883,1882,1881,1880,1879,1878,1877,1876,1875,1874,1873,1872,1871,1870,1869,1868,1867,1866,1865,1864,1863,1862,1861,1860,1859,1858,1857,1856,1855,1854,1853,1852,1851,1850,1849,1848,1847,1846,1845,1844,1843,1842,1841,1840,1839,1838,1837,1836,1835,1834,1833,1832,1831,1830,1829,1828,1827,1826,1825,1824,1823,1822,1821,1820,1819,1818,1817,1816,1815,1814,1813,1812,1811,1810,1809,1808,1807,1806,1805,1804,1803,1802,1801,1800,1799,1798,1797,1796,1795,1794,1793,1792,1791,1790,1789,1788,1787,1786,1785,1784,1783,1782,1781,1780,1779,1778,1777,1776,1775,1774,1773,1772,1771,1770,1769,1768,1767,1766,1765,1764,1763,1762,1761,1760,1759,1758,1757,1756,1755,1754,1753,1752,1751,1750,1749,1748,1747,1746,1745,1744,1743,1742,1741,1740,1739,1738,1737,1736,1735,1734,1733,1732,1731,1730,1729,1728,1727,1726,1725,1724,1723,1722,1721,1720,1719,1718,1717,1716,1715,1714,1713,1712,1711,1710,1709,1708,1707,1706,1705,1704,1703,1702,1701,1700,1699,1698,1697,1696,1695,1694,1693,1692,1691,1690,1689,1688,1687,1686,1685,1684,1683,1682,1681,1680,1679,1678,1677,1676,1675,1674,1673,1672,1671,1670,1669,1668,1667,1666,1665,1664,1663,1662,1661,1660,1659,1658,1657,1656,1655,1654,1653,1652,1651,1650,1649,1648,1647,1646,1645,1644,1643,1642,1641,1640,1639,1638,1637,1636,1635,1634,1633,1632,1631,1630,1629,1628,1627,1626,1625,1624,1623,1622,1621,1620,1619,161 8,1617,1616,1615,1614,1613,1612,1611,1610,1609,1608,1607,1606,1605,1604,1603,1602,1601,1600,1599,1598,1597,1596,1595,1594,1593,1592,1591,1590,1589,1588,1587,1586,1585,1584,1583,1582,1581,1580,1579,1578,1577,1576,1575,1574,1573,1572,1571,1570,1569,1568,1567,1566,1565,1564,1563,1562,1561,1560,1559,1558,1557,1556,1555,1554,1553,1552,1551,1550,1549,1548,1547,1546,1545,1544,1543,1542,1541,1540,1539,1538,1537,1536,1535,1534,1533,1532,1531,1530,1529,1528,1527,1526,1525,1524,1523,1522,1521,1520,1519,1518,1517,1516,1515,1514,1513,1512,1511,1510,1509,1508,1507,1506,1505,1504,1503,1502,1501,1500,1499,1498,1497,1496,1495,1494,1493,1492,1491,1490,1489,1488,1487,1486,1485,1484,1483,1482,1481,1480,1479,1478,1477,1476,1475,1474,1473,1472,1471,1470,1469,1468,1467,1466,1465,1464,1463,1462,1461,1460,1459,1458,1457,1456,1455,1454,1453,1452,1451,1450,1449,1448,1447,1446,1445,1444,1443,1442,1441,1440,1439,1438,1437,1436,1435,1434,1433,1432,1431,1430,1429,1428,1427,1426,1425,1424,1423,1422,1421,1420,1419,1418,1417,1416,1415,1414,1413,1412,1411,1410,1409,1408,1407,1406,1405,1404,1403,1402,1401,1400,1399,1398,1397,1396,1395,1394,1393,1392,1391,1390,1389,1388,1387,1386,1385,1384,1383,1382,1381,1380,1379,1378,1377,1376,1375,1374,1373,1372,1371,1370,1369,1368,1367,1366,1365,1364,1363,1362,1361,1360,1359,1358,1357,1356,1355,1354,1353,1352,1351,1350,1349,1348,1347,1346,1345,1344,1343,1342,1341,1340,1339,1338,1337,1336,1335,1334,1333,1332,1331,1330,1329,1328,1327,1326,1325,1324,1323,1322,1321,1320,1319,1318,1317,1316,1315,1314,1313,1312,1311,1310,1309,1308,1307,1306,1305,1304,1303,1302,1301,1300,1299,1298,1297,1296,1295,1294,1293,1292,1291,1290,1289,1288,1287,1286,1285,1284,1283,1282,1281,1280,1279,1278,1277,1276,1275,1274,1273,1272,1271,1270,1269,1268,1267,1266,1265,1264,1263,1262,1261,1260,1259,1258,1257,1256,1255,1254,1253,1252,1251,1250,1249,1248,1247,1246,1245,1244,1243,1242,1241,1240,1239,1238,1237,1236,1235,1234,1233,1232,1231,1230,1229,1228,1227,1226,1225,1224,1223,1222,1221,1220,1219,1218,1217,1216,1215,1214,1213,1212,1211,1210,1209,1208,1207,1206,1205,1204,1203,1202,1201
M＝1440,N＝2048
1024,1023,1022,1020,1408,1280,1407,1406,1440,1016,1439,1404,1008,1438,1279,1021,1400,992,1278,1019,1436,1392,1018,1015,1276,1405,960,1432,1014,1403,1376,1007,1272,1012,1424,1402,1006,896,1399,1437,991,1264,1004,1344,1398,1017,1277,990,1435,1391,768,1000,1396,1013,959,988,1275,1248,1390,1434,958,1431,1011,1274,984,1005,1375,1388,1271,1010,1401,956,1430,895,1216,1003,1374,976,1384,1270,1423,894,1397,989,1002,952,1428,1263,999,1372,1343,512,1268,1422,987,892,1395,998,1262,944,767,1342,1389,1368,986,957,1394,983,996,1420,888,1247,766,1260,1433,1340,1387,1009,1273,928,982,955,1360,1152,1246,764,975,880,1416,1386,1256,954,1373,980,1336,1001,1383,1269,1429,951,893,974,1 215,1244,760,1371,1382,950,864,997,1267,891,972,1328,1427,1214,943,985,511,1240,1261,1370,948,1380,1421,752,995,890,1341,1266,1367,968,942,887,1426,1393,1212,510,765,981,832,1259,994,927,1366,1232,1339,940,886,1419,1312,736,979,953,1258,1359,763,508,1245,926,879,1208,1385,1151,973,1255,1338,1364,884,936,978,1418,1335,762,1358,949,878,924,1243,1415,759,971,1254,1150,504,1381,704,1200,1334,863,1356,947,876,1242,970,758,920,1414,1213,1327,1369,1252,889,941,1148,967,1239,1379,862,496,946,751,1332,1265,872,1352,756,1326,966,993,939,1238,509,912,1211,885,831,1378,1184,1365,1412,640,750,860,1144,1231,925,938,964,1425,480,1324,1257,1210,735,830,1236,1311,935,883,507,1363,748,977,856,1337,1207,877,1230,923,1136,761,1357,934,882,734,506,1310,828,1320,1362,1253,1206,1149,503,744,922,875,848,1228,1333,969,1417,448,919,932,703,757,1355,1199,732,1241,1308,824,861,874,502,945,1120,1251,1204,1147,918,871,1331,1224,1354,702,965,755,1198,495,728,911,1413,1351,1325,859,1237,1250,1304,500,749,1146,870,816,916,937,1330,754,494,1143,963,700,1183,1377,384,1196,910,858,639,1350,829,1088,1323,1235,855,747,1209,868,720,479,1411,1296,962,933,1142,1229,1182,492,881,800,908,638,696,1192,733,827,854,1322,746,1234,505,1348,921,1135,1309,478,743,1205,1319,847,931,1140,1361,1410,1227,1180,488,826,904,852,636,256,731,873,1134,823,742,917,688,501,447,1307,846,1318,930,476,1203,1226,730,1176,1119,701,1197,822,1223,869,632,727,1353,740,1132,446,915,1306,499,844,1202,1316,472,815,1145,1303,857,909,753,493,672,1249,1118,1222,820,699,726,1329,1195,914,867,498,1168,444,840,1128,814,624,1349,719,1302,383,907,491,853,464,698,1141,1087,1194,866,724,1220,745,1116,1181,961,799,1295,637,695,1191,812,718,440,1321,906,382,1233,477,490,1300,1347,825,851,1086,903,1139,798,487,608,694,1179,1294,741,845,1112,1190,635,716,1133,808,475,850,380,687,929,729,902,1346,432,1138,486,1317,821,796,1084,255,1178,692,1225,634,739,843,1292,1188,474,712,1175,1131,686,631,445,1104,1409,576,1305,900,484,471,376,1201,819,725,254,842,738,1315,792,671,1080,913,497,813,1174,1117,1130,416,839,1221,630,684,1288,443,470,818,1127,697,723,1167,623,1314,1301,670,252,368,865,463,838,1193,811,784,717,1172,628,1115,442,680,1219,468,489,1072,1126,722,905,1166,439,622,381,693,668,462,797,810,836,1299,715,1114,248,1085,807,1218,1189,607,1124,849,352,1111,438,1293,485,620,1164,901,691,460,379,795,714,664,1298,1137,1056,431,806,633,1177,473,685,711,606,1083,1110,240,436,1187,690,483,794,378,1291,616,1345,841,456,899,1160,430,1103,737,804,791,710,375,656,320,575,683,1082,629,253,469,604,1108,1129,482,1173,1186,817,415,1290,1079,898,790,428,1102,669,682,374,708,224,837,574,1287,627,441,467,679,783,251,600,721,414,367,1171,1078,1125,621,461,788,809,667,1313,1100,424,372,1165,835,626,572,466,678,1286,1071,782,250,1113,366,437,1170,412,666,592,1076,247,619,459,192,1123,713,834,676,805,663,1096,351,1163,1070,780,568,1284,1217,364,435,605,689,618,408,458,246,1109,7 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6,3905,3904,3903,3902,3901,3900,3899,3898,3897,3896,3895,3894,3893,3892,3891,3890,3889,3888,3887,3886,3885,3884,3883,3882,3881,3880,3879,3878,3877,3876,3875,3874,3873,3872,3871,3870,3869,3868,3867,3866,3865,3864,3863,3862,3861,3860,3859,3858,3857,3856,3855,3854,3853,3852,3851,3850,3849,3848,3847,3846,3845,3844,3843,3842,3841,3840,3839,3838,3837,3836,3835,3834,3833,3832,3831,3830,3829,3828,3827,3826,3825,3824,3823,3822,3821,3820,3819,3818,3817,3816,3815,3814,3813,3812,3811,3810,3809,3808,3807,3806,3805,3804,3803,3802,3801,3800,3799,3798,3797,3796,3795,3794,3793,3792,3791,3790,3789,3788,3787,3786,3785,3784,3783,3782,3781,3780,3779,3778,3777,3776,3775,3774,3773,3772,3771,3770,3769,3768,3767,3766,3765,3764,3763,3762,3761,3760,3759,3758,3757,3756,3755,3754,3753,3752,3751,3750,3749,3748,3747,3746,3745,3744,3743,3742,3741,3740,3739,3738,3737,3736,3735,3734,3733,3732,3731,3730,3729,3728,3727,3726,3725,3724,3723,3722,3721,3720,3719,3718,3717,3716,3715,3714,3713,3712,3711,3710,3709,3708,3707,3706,3705,3704,3703,3702,3701,3700,3699,3698,3697,3696,3695,3694,3693,3692,3691,3690,3689,3688,3687,3686,3685,3684,3683,3682,3681,3680,3679,3678,3677,3676,3675,3674,3673,3672,3671,3670,3669,3668,3667,3666,3665,3664,3663,3662,3661,3660,3659,3658,3657,3656,3655,3654,3653,3652,3651,3650,3649,3648,3647,3646,3645,3644,3643,3642,3641,3640,3639,3638,3637,3636,3635,3634,3633,3632,3631,3630,3629,3628,3627,3626,3625,3624,3623,3622,3621,3620,3619,3618,3617,3616,3615,3614,3613,3612,3611,3610,3609,3608,3607,3606,3605,3604,3603,3602,3601,3600,3599,3598,3597,3596,3595,3594,3593,3592,3591,3590,3589,3588,3587,3586,3585,3584,3583,3582,3581,3580,3579,3578,3577,3576,3575,3574,3573,3572,3571,3570,3569,3568,3567,3566,3565,3564,3563,3562,3561,3560,3559,3558,3557,3556,3555,3554,3553,3552,3551,3550,3549,3548,3547,3546,3545,3544,3543,3542,3541,3540,3539,3538,3537,3536,3535,3534,3533,3532,3531,3530,3529,3528,3527,3526,3525,3524,3523,3522,3521,3520,3519,3518,3517,3516,3515,3514,3513,3512,3511,3510,3509,3508,3507,3506,3505,3504,3503,3502,3501,3500,3499,3498,3497,3496,3495,3494,3493,3492,3491,3490,3489,3488,3487,3486,3485,3484,3483,3482,3481,3480,3479,3478,3477,3476,3475,3474,3473,3472,3471,3470,3469,3468,3467,3466,3465,3464,3463,3462,3461,3460,3459,3458,3457,3456,3455,3454,3453,3452,3451,3450,3449,3448,3447,3446,3445,3444,3443,3442,3441,3440,3439,3438,3437,3436,3435,3434,3433,3432,3431,3430,3429,3428,3427,3426,3425,3424,3423,3422,3421,3420,3419,3418,3417,3416,3415,3414,3413,3412,3411,3410,3409,3408,3407,3406,3405,3404,3403,3402,3401,3400,3399,3398,3397,3396,3395,3394,3393,3392,3391,3390,3389,3388,3387,3386,3385,3384,3383,3382,3381,3380,3379,3378,3377,3376,3375,3374,3373,3372,3371,3370,3369,3368,3367,3366,3365,3364,3363,3362,3361,3360,3359,3358,3357,3356,3355,3354,3353,3352,3351,3350,3349,3348,3347,3346,3345,3344,3343,3342,3341,3340,3339,3338,3337,3336,3335,3334,3333,3332,3331,3330,3329,3328,3327,3326,3325,3324,3323,3322,332 1,3320,3319,3318,3317,3316,3315,3314,3313,3312,3311,3310,3309,3308,3307,3306,3305,3304,3303,3302,3301,3300,3299,3298,3297,3296,3295,3294,3293,3292,3291,3290,3289,3288,3287,3286,3285,3284,3283,3282,3281,3280,3279,3278,3277,3276,3275,3274,3273,3272,3271,3270,3269,3268,3267,3266,3265,3264,3263,3262,3261,3260,3259,3258,3257,3256,3255,3254,3253,3252,3251,3250,3249,3248,3247,3246,3245,3244,3243,3242,3241,3240,3239,3238,3237,3236,3235,3234,3233,3232,3231,3230,3229,3228,3227,3226,3225,3224,3223,3222,3221,3220,3219,3218,3217,3216,3215,3214,3213,3212,3211,3210,3209,3208,3207,3206,3205,3204,3203,3202,3201,3200,3199,3198,3197,3196,3195,3194,3193,3192,3191,3190,3189,3188,3187,3186,3185,3184,3183,3182,3181,3180,3179,3178,3177,3176,3175,3174,3173,3172,3171,3170,3169,3168,3167,3166,3165,3164,3163,3162,3161,3160,3159,3158,3157,3156,3155,3154,3153,3152,3151,3150,3149,3148,3147,3146,3145,3144,3143,3142,3141,3140,3139,3138,3137,3136,3135,3134,3133,3132,3131,3130,3129,3128,3127,3126,3125,3124,3123,3122,3121,3120,3119,3118,3117,3116,3115,3114,3113,3112,3111,3110,3109,3108,3107,3106,3105,3104,3103,3102,3101,3100,3099,3098,3097,3096,3095,3094,3093,3092,3091,3090,3089,3088,3087,3086,3085,3084,3083,3082,3081,3080,3079,3078,3077,3076,3075,3074,3073,3072,3071,3070,3069,3068,3067,3066,3065,3064,3063,3062,3061,3060,3059,3058,3057,3056,3055,3054,3053,3052,3051,3050,3049,3048,3047,3046,3045,3044,3043,3042,3041,3040,3039,3038,3037,3036,3035,3034,3033,3032,3031,3030,3029,3028,3027,3026,3025,3024,3023,3022,3021,3020,3019,3018,3017,3016,3015,3014,3013,3012,3011,3010,3009,3008,3007,3006,3005,3004,3003,3002,3001,3000,2999,2998,2997,2996,2995,2994,2993,2992,2991,2990,2989,2988,2987,2986,2985,2984,2983,2982,2981,2980,2979,2978,2977,2976,2975,2974,2973,2972,2971,2970,2969,2968,2967,2966,2965,2964,2963,2962,2961,2960,2959,2958,2957,2956,2955,2954,2953,2952,2951,2950,2949,2948,2947,2946,2945,2944,2943,2942,2941,2940,2939,2938,2937,2936,2935,2934,2933,2932,2931,2930,2929,2928,2927,2926,2925,2924,2923,2922,2921,2920,2919,2918,2917,2916,2915,2914,2913,2912,2911,2910,2909,2908,2907,2906,2905,2904,2903,2902,2901,2900,2899,2898,2897,2896,2895,2894,2893,2892,2891,2890,2889,2888,2887,2886,2885,2884,2883,2882,2881,2880,2879,2878,2877,2876,2875,2874,2873,2872,2871,2870,2869,2868,2867,2866,2865,2864,2863,2862,2861,2860,2859,2858,2857,2856,2855,2854,2853,2852,2851,2850,2849,2848,2847,2846,2845,2844,2843,2842,2841,2840,2839,2838,2837,2836,2835,2834,2833,2832,2831,2830,2829,2828,2827,2826,2825,2824,2823,2822,2821,2820,2819,2818,2817,2816,2815,2814,2813,2812,2811,2810,2809,2808,2807,2806,2805,2804,2803,2802,2801,2800,2799,2798,2797,2796,2795,2794,2793,2792,2791,2790,2789,2788,2787,2786,2785,2784,2783,2782,2781,2780,2779,2778,2777,2776,2775,2774,2773,2772,2771,2770,2769,2768,2767,2766,2765,2764,2763,2762,2761,2760,2759,2758,2757,2756,2755,2754,2753,2752,2751,2750,2749,2748,2747,2746,2745,2744,2743,2742,2741,2740,2739,2738,2737,273 6,2735,2734,2733,2732,2731,2730,2729,2728,2727,2726,2725,2724,2723,2722,2721,2720,2719,2718,2717,2716,2715,2714,2713,2712,2711,2710,2709,2708,2707,2706,2705,2704,2703,2702,2701,2700,2699,2698,2697,2696,2695,2694,2693,2692,2691,2690,2689,2688,2687,2686,2685,2684,2683,2682,2681,2680,2679,2678,2677,2676,2675,2674,2673,2672,2671,2670,2669,2668,2667,2666,2665,2664,2663,2662,2661,2660,2659,2658,2657,2656,2655,2654,2653,2652,2651,2650,2649,2648,2647,2646,2645,2644,2643,2642,2641,2640,2639,2638,2637,2636,2635,2634,2633,2632,2631,2630,2629,2628,2627,2626,2625,2624,2623,2622,2621,2620,2619,2618,2617,2616,2615,2614,2613,2612,2611,2610,2609,2608,2607,2606,2605,2604,2603,2602,2601,2600,2599,2598,2597,2596,2595,2594,2593,2592,2591,2590,2589,2588,2587,2586,2585,2584,2583,2582,2581,2580,2579,2578,2577,2576,2575,2574,2573,2572,2571,2570,2569,2568,2567,2566,2565,2564,2563,2562,2561,2560,2559,2558,2557,2556,2555,2554,2553,2552,2551,2550,2549,2548,2547,2546,2545,2544,2543,2542,2541,2540,2539,2538,2537,2536,2535,2534,2533,2532,2531,2530,2529,2528,2527,2526,2525,2524,2523,2522,2521,2520,2519,2518,2517,2516,2515,2514,2513,2512,2511,2510,2509,2508,2507,2506,2505,2504,2503,2502,2501,2500,2499,2498,2497,2496,2495,2494,2493,2492,2491,2490,2489,2488,2487,2486,2485,2484,2483,2482,2481,2480,2479,2478,2477,2476,2475,2474,2473,2472,2471,2470,2469,2468,2467,2466,2465,2464,2463,2462,2461,2460,2459,2458,2457,2456,2455,2454,2453,2452,2451,2450,2449,2448,2447,2446,2445,2444,2443,2442,2441,2440,2439,2438,2437,2436,2435,2434,2433,2432,2431,2430,2429,2428,2427,2426,2425,2424,2423,2422,2421,2420,2419,2418,2417,2416,2415,2414,2413,2412,2411,2410,2409,2408,2407,2406,2405,2404,2403,2402,2401
表3
M＝48,N＝64
48,32,47,46,31,44,30,40,28,45,24,43,42,39,29,16,38,27,36,26,23,22,41,20,15,37,14,25,35,12,34,21,8,19,18,13,11,10,7,33,6,4,17,9,5,3,2,1,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49
M＝72,N＝128
64,63,62,60,56,48,61,72,71,32,59,70,58,55,68,54,47,52,46,31,44,57,30,40,53,28,69,51,24,45,67,50,43,16,66,29,42,39,27,38,26,36,23,49,22,15,20,41,14,65,37,12,25,35,8,21,34,19,13,18,11,10,7,33,6,4,17,9,5,3,2,1,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73
M＝96,N＝128
96,64,95,94,92,63,62,88,80,60,93,56,91,90,48,87,61,86,79,59,84,78,58,32,55,76,54,89,47,72,52,85,46,83,44,77,57,82,31,40,75,53,30,74,51,71,28,45,50,70,24,43,68,42,16,81,39,29,38,27,73,36,26,23,49,69,22,67,41,15,20,14,66,37,12,35,25,8,34,21,19,13,18,65,11,10,7,33,6,4,17,9,5,3,2,1,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97
M＝120,N＝128
120,112,96,119,64,118,111,116,110,108,95,94,117,104,92,115,63,109,114,62,88,107,60,106,80,93,103,56,91,102,90,48,61,100,87,113,86,59,32,79,58,84,105,55,78,54,101,76,89,47,52,99,46,72,85,98,31,44,83,57,30,77,82,40,53,28,75,51,74,24,45,71,50,70,43,16,97,42,29,68,39,27,81,38,26,23,36,73,22,49,69,15,20,41,14,67,12,37,66,25,35,8,21,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,128,127,126,125,124,123,122,121
M＝144,N＝256
128,127,126,124,120,112,125,144,143,96,123,142,122,119,64,140,118,111,116,136,110,95,108,121,94,104,63,117,92,141,62,115,88,109,139,114,60,107,80,138,56,93,106,135,103,91,134,48,102,90,61,100,87,132,113,32,86,59,79,58,84,105,55,78,137,54,101,76,47,89,52,99,72,46,133,85,98,31,44,57,83,30,131,77,40,82,53,28,130,75,51,24,74,71,45,50,97,70,16,43,68,29,42,81,39,27,38,26,73,36,23,49,129,22,69,15,20,41,67,14,66,12,37,25,8,35,34,21,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145
M＝160,N＝256
128,127,126,124,120,160,159,158,156,112,125,152,96,123,144,122,119,157,64,118,155,111,116,154,110,151,95,108,121,150,94,104,143,117,148,92,63,142,115,62,109,88,140,114,153,60,107,80,136,106,93,56,149,103,91,102,48,147,90,141,100,61,87,146,113,86,139,59,32,79,105,84,58,138,55,78,135,101,54,76,134,47,89,99,52,72,46,132,98,85,145,44,31,83,57,77,30,40,82,137,53,75,28,51,74,133,24,71,45,50,97,70,131,43,16,68,42,130,29,39,81,27,38,73,26,36,23,49,69,22,15,41,20,67,14,66,37,129,12,25,35,8,34,21,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241, 240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161
M＝180,N＝256
128,127,126,124,176,160,175,180,174,120,179,172,159,112,125,178,158,168,96,123,156,122,119,173,152,118,64,171,111,116,110,170,157,144,167,95,108,121,177,166,155,94,104,117,154,92,164,151,63,115,88,150,109,114,62,169,143,107,148,80,60,93,106,142,165,103,56,91,140,102,153,163,90,48,87,100,136,149,162,61,113,86,32,79,59,147,84,105,141,78,58,146,55,101,76,139,54,89,99,47,138,72,52,135,85,98,46,161,134,31,83,44,77,57,30,82,132,40,145,75,53,28,74,51,71,24,45,137,50,70,97,43,16,133,68,29,42,81,39,131,27,38,73,26,130,23,36,49,69,22,15,67,20,41,14,66,37,12,25,35,8,21,129,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181
M＝192,N＝256
192,128,191,190,188,127,184,126,176,124,189,160,187,120,186,183,112,182,125,175,96,180,123,174,122,159,119,172,185,158,118,168,111,181,156,116,64,110,179,152,173,95,108,178,121,171,94,144,104,157,170,117,92,167,155,115,166,88,109,63,154,114,151,164,62,107,80,177,150,93,106,60,143,103,148,169,91,142,102,56,90,165,87,140,100,48,153,113,86,61,163,136,79,149,32,84,59,162,105,78,58,147,55,101,141,76,146,89,54,99,139,72,47,85,52,98,138,46,135,83,31,44,77,134,57,82,161,30,75,40,132,53,28,74,145,71,51,24,45,70,50,97,137,43,16,68,29,42,133,81,39,27,38,131,73,26,23,36,130,69,49,22,15,67,20,41,14,66,37,12,25,35,8,21,34,129,19,13,18,65,11,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193
M＝240,N＝256
240,224,192,239,238,128,223,236,232,222,220,191,237,216,190,235,188,234,127,231,221,208,184,230,126,219,218,228,124,215,176,189,214,120,187,212,23 3,160,207,186,183,112,206,125,229,182,204,217,123,227,180,175,96,122,226,200,213,174,119,211,118,159,172,64,185,158,210,205,111,116,168,181,110,203,156,179,202,95,108,152,199,173,178,121,94,198,104,171,225,117,92,144,63,170,157,196,115,167,62,88,209,109,155,166,114,60,154,107,151,164,80,201,106,93,56,150,103,177,197,91,143,102,148,169,48,90,142,195,87,100,61,165,140,86,194,113,59,32,153,79,163,58,84,136,55,78,105,149,162,54,76,101,147,47,52,89,141,99,146,46,72,139,85,98,31,44,138,83,57,30,135,77,193,40,82,53,134,28,75,161,51,74,132,24,45,71,50,145,70,43,16,97,42,29,68,39,137,27,38,81,133,26,23,36,73,131,22,49,69,130,15,20,41,14,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241
M＝288,N＝512
256,255,254,252,248,240,253,288,287,224,251,286,250,247,192,284,246,239,244,128,280,238,223,236,249,272,222,232,191,245,220,285,190,243,216,237,283,242,188,127,208,235,282,126,184,279,221,234,231,124,278,219,176,230,271,218,120,189,228,215,276,241,160,187,214,270,112,207,186,212,233,125,183,206,268,96,281,182,229,123,204,175,217,264,180,227,122,200,174,119,64,277,213,226,159,172,118,185,211,111,275,158,205,116,168,269,210,110,181,156,274,203,95,108,267,179,152,202,121,94,173,199,178,104,266,225,198,144,63,171,92,117,263,196,170,157,62,115,88,167,209,262,109,155,60,114,166,80,260,107,154,201,164,151,56,273,106,93,177,103,150,197,48,143,91,102,148,169,195,142,265,90,61,100,87,194,32,165,113,140,59,86,153,261,79,163,136,58,84,105,55,78,162,149,259,54,101,76,147,47,258,89,141,52,146,99,72,46,193,139,98,85,31,44,138,30,57,135,83,40,77,161,82,134,28,53,75,132,24,51,74,145,71,45,16,50,97,257,70,43,137,68,29,42,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385,384,383,382,381,380,379,378,377,376,375,374,373,372,371,370,369,368,367,366,365,364,363,362,361,360,359,358,357,356,355,354,353,352,351,350,349,348,347,346,345,344,343,342,341,340,339,338,337,336,335,334,333,332,331,330,329,328,327,326,325,324,323,322,321,320,319,318,317,316,315,314,313,312,311,310,309,308,307,306,305,304,303,302,301,300,299,298,297,296,295,294,293,292,291,290,289
M＝300,N＝512
256,255,254,252,248,240,288,300,296,253,224,251,250,287,247,192,246,286,239,299,244,128,238,284,223,298,236,249,222,232,280,295,245,191,220,294,190,243,216,237,242,272,188,127,285,235,208,126,184,221,234,292,231,283,124,219,176,230,282,297,218,189,120,228,215,279,241,160,214,187,278,112,207,212,186,233,293,125,183,206,271,276,96,229,182,204,123,270,175,217,291,180,227,122,200,174,119,213,64,226,281,268,159,290,172,118,211,185,111,158,205,264,116,168,277,210,110,181,156,203,95,275,108,179,202,152,121,199,173,94,269,178,104,274,225,198,144,171,92,117,63,196,157,170,267,62,115,209,167,88,109,289,155,266,114,166,60,263,80,201,154,107,164,151,56,93,177,106,262,150,103,197,143,91,48,102,148,260,169,195,273,142,90,61,100,87,194,165,113,32,140,86,59,153,79,163,136,265,84,58,105,55,149,78,162,54,76,101,261,147,47,89,141,52,146,99,72,46,193,259,139,98,85,31,44,138,258,83,135,57,30,77,40,161,82,134,28,53,75,132,24,74,51,145,71,45,50,97,16,70,43,137,68,29,42,81,39,133,257,27,38,131,26,73,23,36,22,49,130,15,69,20,14,41,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385,384,383,382,381,380,379,378,377,376,375,374,373,372,371,370,369,368,367,366,365,364,363,362,361,360,359,358,357,356,355,354,353,352,351,350,349,348,347,346,345,344,343,342,341,340,339,338,337,336,335,334,333,332,331,330,329,328,327,326,325,324,323,322,321,320,319,318,317,316,315,314,313,312,311,310,309,308,307,306,305,304,303,302,301
M＝360,N＝512
256,255,254,252,352,320,351,350,360,248,359,348,240,319,358,253,344,318,224,251,356,316,250,336,247,349,192,246,312,347,239,244,346,238,304,343,317,223,357,236,128,249,342,222,315,232,335,355,245,191,340,220,314,288,334,311,243,190,354,216,237,332,242,310,345,188,235,303,208,308,234,221,184,127,328,341,231,302,219,126,230,339,176,300,313,218,287,333,189,124,228,215,338,241,286,296,160,214,187,331,309,120,207,353,284,186,212,233,330,307,183,206,112,327,301,280,306,182,229,125,204,326,175,217,299,180,227,96,123,272,200,174,324,298,213,226,122,285,337,295,159,119,172,211,185,64,294,283,158,118,205,168,329,210,111,181,282,292,156,116,203,279,305,110,179,325,202,152,2 78,173,199,95,108,178,271,121,297,323,198,225,171,276,94,144,104,270,157,170,117,322,196,63,92,293,167,209,268,155,115,62,281,166,88,109,291,154,114,201,264,60,151,164,107,290,277,80,177,150,197,106,56,93,143,275,103,148,169,269,91,195,102,142,48,274,90,194,61,165,267,321,100,87,140,153,113,32,86,59,266,163,136,263,79,149,58,162,84,105,289,55,78,262,147,54,101,141,76,260,47,146,89,52,99,273,139,72,46,193,85,98,138,31,44,135,265,57,83,30,161,77,134,40,82,53,28,261,75,132,145,51,74,24,45,71,259,50,97,70,258,16,137,43,29,68,42,39,133,81,27,38,131,26,73,36,23,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385,384,383,382,381,380,379,378,377,376,375,374,373,372,371,370,369,368,367,366,365,364,363,362,361
M＝384,N＝512
384,256,383,382,380,255,376,254,368,381,252,352,379,248,378,375,320,240,374,253,367,372,224,366,251,351,250,364,247,377,350,192,360,246,373,319,348,239,244,318,371,238,344,365,370,316,223,236,363,336,249,222,349,362,312,232,359,128,245,191,220,347,358,304,190,243,346,317,216,343,237,356,242,188,369,288,342,315,235,208,335,314,340,221,234,184,361,311,231,334,127,219,310,230,357,332,176,303,126,218,345,189,308,215,228,355,302,328,124,241,341,160,214,187,354,287,300,207,186,339,313,120,212,233,286,183,333,206,296,338,309,182,112,284,229,331,204,175,125,217,307,180,330,227,280,200,301,174,327,96,123,213,306,226,159,326,299,172,122,353,272,211,185,119,158,64,205,285,298,324,168,210,118,295,181,156,337,203,283,111,294,116,179,202,282,110,152,173,199,329,279,292,178,95,108,305,198,171,278,225,121,144,94,325,271,157,170,104,196,276,167,297,117,63,92,323,270,209,155,166,62,115,293,322,88,154,109,268,201,151,114,164,281,60,291,107,177,80,150,264,197,277,93,56,106,143,290,103,148,169,195,91,142,275,102,48,269,165,90,194,61,140,274,87,100,153,267,113,32,163,86,59,136,321,79,149,266,162,58,84,105,263,55,78,147,262,54,141,289,101,76,146,47,89,52,139,99,260,72,46,193,85,273,138,98,31,135,44,57,83,30,77,134,161,265,40,82,53,28,75,132,261,145,51,74,24,45,71,50,259,137,97,70,16,43,258,29,42,68,133,39,81,27,38,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496, 495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385
M＝400,N＝512
384,256,383,382,380,255,376,254,400,368,252,381,399,352,379,248,378,398,375,320,240,374,253,396,367,372,224,251,366,351,250,392,364,247,377,350,192,360,246,373,319,348,239,244,371,397,318,238,344,365,370,223,316,236,395,363,249,336,222,349,362,128,312,232,359,394,245,191,220,347,391,358,243,304,190,346,216,237,317,343,356,242,390,188,369,342,235,315,288,208,335,388,234,221,314,340,184,361,231,311,334,127,219,230,310,357,126,176,332,218,303,345,189,215,228,308,355,124,393,328,302,241,214,187,341,160,354,287,207,120,300,186,212,339,233,313,183,389,206,286,333,338,296,112,182,309,229,204,284,125,331,387,175,217,180,307,227,330,96,123,200,174,280,301,327,213,306,386,226,122,159,172,119,326,299,211,185,353,272,64,158,205,118,298,285,168,210,324,295,181,111,156,203,337,116,283,294,110,179,202,152,282,173,199,95,329,178,279,292,108,121,198,171,305,94,225,278,144,104,325,157,170,117,271,196,63,92,167,276,297,209,323,155,270,115,62,166,385,88,109,154,293,114,322,268,201,151,60,164,107,281,80,177,291,150,93,106,264,197,56,103,143,277,290,148,169,91,195,102,142,48,275,90,61,165,269,87,194,100,140,274,153,113,86,32,59,163,267,136,79,149,58,84,321,162,105,266,55,78,263,147,54,101,141,76,262,289,47,146,89,52,99,139,72,46,260,85,193,98,138,31,273,44,135,83,57,30,77,134,40,82,161,53,265,28,75,132,51,74,145,24,261,45,71,50,70,43,259,97,16,137,29,42,258,68,39,133,81,27,38,131,26,73,36,23,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401
M＝480,N＝512
480,448,384,479,478,476,447,256,472,446,464,444,477,383,440,475,382,474,432,471,380,445,470,255,463,376,443,468,254,462,442,439,416,368,252,460,381,438,473,431,379,456,436,248,469,430,352,378,375,467,240,428,461,374,253,4 41,415,466,320,367,424,459,372,251,414,437,366,224,458,250,412,435,455,247,364,429,351,434,454,246,408,377,192,427,360,350,239,244,373,452,426,400,238,348,423,319,413,371,465,422,365,128,236,318,344,411,223,370,249,363,420,457,410,316,222,232,407,336,362,245,433,359,349,220,453,406,312,191,243,358,399,347,190,425,404,237,451,216,242,398,304,346,356,343,235,188,317,450,421,127,396,208,342,369,234,315,221,419,231,409,288,126,184,335,340,314,392,361,219,230,311,334,418,405,124,176,218,310,357,228,332,215,189,403,303,120,397,345,308,214,355,241,187,402,302,328,160,207,395,354,341,212,186,112,233,300,183,206,287,394,125,339,449,313,391,182,286,333,204,229,296,123,338,175,96,390,309,180,217,284,331,227,122,174,200,417,119,307,388,330,213,226,280,301,327,172,159,118,64,306,211,185,326,111,158,299,401,205,116,168,272,210,110,353,298,181,156,285,324,203,295,393,108,179,95,202,283,294,152,173,199,337,121,389,94,178,282,104,198,292,279,171,117,329,144,92,387,63,225,170,278,157,196,305,167,115,62,271,325,88,386,109,155,276,166,114,209,270,297,60,107,154,323,80,151,164,268,106,201,93,293,56,322,150,103,177,281,91,143,102,291,197,264,148,48,90,142,277,169,290,87,100,61,195,275,140,86,165,194,59,32,113,269,79,153,274,58,84,163,136,55,78,267,105,385,149,162,54,266,76,101,147,47,263,52,321,89,141,99,46,72,146,262,139,85,98,31,44,289,260,138,83,57,30,135,77,40,193,82,273,53,134,28,75,51,74,132,24,161,45,71,265,50,70,43,145,261,16,97,42,29,68,137,39,27,259,38,81,26,133,258,23,36,73,131,22,49,69,15,130,20,41,14,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481
M＝576,N＝1024
512,511,510,508,504,496,509,576,575,480,507,574,506,503,448,572,502,495,500,384,568,494,479,492,560,505,478,256,488,447,501,476,573,446,499,544,472,493,571,498,444,383,464,491,570,382,440,477,567,490,487,380,566,475,432,255,486,559,474,376,445,254,484,471,564,416,497,558,470,443,252,368,463,543,442,468,489,381,439,462,556,248,352,569,438,485,542,460,379,431,473,240,552,436,378,483,456,430,375,540,565,320,253,469,482,415,224,374,428,251,467,441,367,563,414,536,461,372,424,557,466,250,366,412,437,562,247,192,459,351,528,364,555,246,408,435,458,377,350,455,429,239,541,434,360,128,244,554,481,400,454,348,319,427,238,373,551,452,223,413,426,539,318,236,344,371,423,465,550,365,249,222,411,316,370,422,538,232,336,548,535,410,363,457,220,191,420,245,407,312,561,349,433,362,534,190,406,359,453,216,243,399,304,527,347,237,358,404,188,425,242,532,451,127,398,553,346,208,317,356,526,343,235,450,288,126,184,396,421,369,221,234,342,315,409,524,231,549,335,124,419,392,340,176,314,219,361,537,230,311,334,405,418,120,520,218,547,189,310,228,332,21 5,357,160,403,303,241,345,546,533,397,308,214,112,187,402,328,355,302,207,449,395,212,186,354,341,287,233,531,125,183,206,300,96,394,525,286,339,391,313,182,530,204,123,229,296,333,417,175,338,390,284,217,180,122,523,64,309,200,227,331,174,119,388,280,226,213,330,159,307,401,522,118,172,327,301,519,306,111,158,272,211,353,185,326,116,168,205,299,545,393,110,210,518,156,324,285,298,181,95,203,108,295,337,152,389,516,94,202,283,179,294,121,199,104,173,529,387,282,178,144,329,225,92,292,198,63,279,117,171,386,305,278,62,196,88,157,325,170,271,115,167,209,521,276,60,109,297,323,155,270,114,80,166,322,154,107,56,201,268,164,151,293,517,93,106,177,281,150,264,103,48,197,291,143,91,515,102,148,290,385,277,195,142,169,32,90,61,514,100,87,194,275,140,113,165,269,86,59,274,153,79,136,321,163,58,84,267,55,78,105,162,149,266,54,263,76,47,101,147,289,262,52,141,72,89,46,146,99,260,193,31,139,44,98,85,273,30,513,138,40,135,83,57,77,28,82,53,134,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937,936,935,934,933,932,931,930,929,928,927,926,925,924,923,922,921,920,919,918,917,916,915,914,913,912,911,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,839,838,837,836,835,834,833,832,831,830,829,828,827,826,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811,810,809,808,807,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,718,717,716,715,714,713,712,711,710,709,708,707,706,705,704,703,702,701,700,699,698,697,696,695,694,693,692,691,690,689,688,687,686,685,684,683,682,681,680,679,678,677,676,675,674,673,672,671,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,609,608,607,606,605,604,603,602,601,600,599,598,597,596,595,594,593,592,591,590,589,588,58 7,586,585,584,583,582,581,580,579,578,577
M＝600,N＝1024
512,511,510,508,504,496,576,600,592,509,480,507,506,575,503,448,502,574,495,599,500,384,494,572,598,479,492,505,478,256,488,568,596,501,476,447,591,446,499,472,590,493,560,498,444,383,464,491,573,588,440,382,477,490,487,571,380,544,475,432,255,486,597,570,474,445,376,484,471,254,567,416,497,584,443,470,595,252,368,463,566,442,468,489,439,381,462,559,248,594,589,352,564,438,485,460,379,431,473,558,240,436,483,378,587,456,430,375,320,253,469,556,482,415,543,569,428,374,224,586,441,467,251,414,367,461,552,372,424,542,466,250,583,366,437,412,565,192,247,459,351,540,364,435,582,408,458,246,377,563,429,455,350,239,434,593,360,557,481,244,400,454,536,427,580,319,373,348,128,562,238,413,452,426,318,223,555,423,371,465,344,236,365,528,411,249,222,422,316,370,554,585,232,336,410,541,457,363,551,420,407,191,220,245,312,433,349,362,406,550,190,359,453,539,216,243,399,304,347,581,237,404,358,425,188,451,242,548,538,398,346,127,317,208,356,561,343,235,535,450,288,421,396,184,369,579,126,221,315,342,234,409,534,231,335,419,392,578,124,314,340,176,527,361,219,553,311,405,230,418,334,532,218,189,120,526,310,228,357,332,403,215,160,303,549,241,397,345,308,402,187,214,355,524,328,112,302,207,449,395,537,186,212,354,341,547,287,233,183,300,125,206,394,520,96,391,286,313,339,546,182,204,229,296,333,533,123,417,175,338,390,284,217,180,309,122,227,200,331,64,174,388,119,531,280,577,307,226,213,330,401,159,172,525,327,301,118,530,306,158,185,211,353,111,272,326,168,116,299,205,393,523,210,156,110,324,285,298,181,203,95,295,522,337,108,389,152,519,283,179,202,294,94,121,545,199,173,387,104,178,282,329,144,225,292,518,279,198,92,63,171,386,117,305,278,196,157,62,325,170,516,88,271,167,115,209,276,529,60,297,109,155,323,270,166,114,80,154,322,201,268,107,164,56,293,151,521,93,177,281,106,150,264,103,291,197,48,143,91,148,102,290,277,385,169,142,195,517,90,32,61,100,87,194,275,140,165,113,269,59,86,274,515,153,136,79,321,163,58,267,84,514,55,105,162,149,78,266,54,263,76,101,147,47,289,262,52,141,89,72,146,46,99,260,193,31,139,44,98,85,273,30,138,135,40,57,83,28,134,161,77,82,265,513,24,53,132,75,16,261,74,51,145,71,45,50,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937,936,935,934,933,932,931,930 ,929,928,927,926,925,924,923,922,921,920,919,918,917,916,915,914,913,912,911,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,839,838,837,836,835,834,833,832,831,830,829,828,827,826,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811,810,809,808,807,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,718,717,716,715,714,713,712,711,710,709,708,707,706,705,704,703,702,701,700,699,698,697,696,695,694,693,692,691,690,689,688,687,686,685,684,683,682,681,680,679,678,677,676,675,674,673,672,671,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,609,608,607,606,605,604,603,602,601
M＝720,N＝1024
512,511,510,508,704,640,703,702,720,504,719,700,496,639,718,509,696,480,638,507,716,688,506,636,503,701,448,712,502,632,699,495,672,500,698,494,384,695,624,479,717,492,637,694,505,478,715,488,687,635,692,608,501,447,476,686,714,634,499,446,256,711,631,472,493,671,684,498,697,444,383,630,710,491,464,670,680,623,382,477,490,576,693,440,628,487,668,708,622,475,380,691,486,432,474,607,664,685,620,445,690,471,484,376,633,497,255,606,416,470,683,443,713,616,463,629,368,656,254,682,442,468,669,604,489,381,439,679,462,709,627,575,252,667,438,352,485,600,678,379,621,460,626,431,473,574,707,666,248,436,483,378,676,663,619,456,430,375,689,469,592,572,320,482,706,415,662,618,605,374,240,428,615,467,441,367,568,253,414,655,461,660,603,681,372,424,466,614,366,437,224,412,654,251,459,602,560,351,677,612,599,435,364,250,458,625,573,652,408,377,429,455,247,665,350,598,434,675,192,360,544,454,571,246,481,427,591,648,400,373,319,348,596,661,617,674,239,413,426,570,452,244,590,318,371,423,567,465,344,238,659,128,365,613,705,411,370,422,588,566,223,316,653,601,658,236,410,363,336,457,611,249,559,407,420,222,564,584,651,349,312,362,433,232,597,558,610,406,359,453,245,220,191,650,347,399,543,358,304,595,647,404,556,425,243,451,190,569,346,398,216,589,317,542,237,673,343,356,594,646,242,450,552,421,369,188,288,396,127,342,315,565,587,235,409,208,540,644,335,419,126,314,392,221,184,340,234,586,657,361,563,311,231,405,334,5 83,536,418,557,219,124,562,310,230,357,609,176,582,403,332,303,649,218,345,555,397,528,189,308,215,228,120,355,402,580,328,302,241,541,554,160,395,341,214,593,187,354,551,449,645,287,112,207,300,394,539,212,186,339,313,233,550,391,286,125,183,206,333,643,585,296,538,338,417,96,390,548,535,309,182,229,284,123,204,331,642,561,217,175,581,388,534,180,307,227,122,330,280,200,401,174,119,301,327,527,213,64,306,226,532,553,159,579,353,118,326,172,272,299,526,211,185,393,111,158,205,578,285,298,116,324,168,549,210,295,524,110,337,181,156,537,203,389,283,95,294,547,108,179,520,202,152,282,121,329,387,199,173,94,533,292,279,546,178,104,305,641,225,198,386,144,171,278,63,117,92,325,531,271,157,196,525,170,62,276,297,115,167,88,209,530,323,270,109,155,114,60,166,523,577,322,293,268,80,107,154,201,151,164,281,522,56,93,106,291,177,519,264,150,103,197,277,290,545,143,91,48,102,518,148,169,195,385,90,142,275,61,100,87,516,269,194,32,165,113,140,274,86,59,529,153,267,79,163,321,136,58,84,105,55,266,149,78,162,263,521,54,101,76,147,289,47,262,89,141,52,517,146,99,72,46,260,193,139,85,98,31,273,515,44,138,30,57,83,40,135,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937,936,935,934,933,932,931,930,929,928,927,926,925,924,923,922,921,920,919,918,917,916,915,914,913,912,911,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,839,838,837,836,835,834,833,832,831,830,829,828,827,826,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811,810,809,808,807,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721
M＝768,N＝1024
768,512,767,766,764,760,511,510,752,765,508,736,763,504,762,759,704,496,758,509,751,756,640,750,480,507,735,748,506,761,734,503,744,448,757,703,50 2,732,495,702,755,500,728,749,494,384,754,700,639,747,479,720,492,638,733,746,505,696,478,743,488,731,636,501,742,447,688,476,730,701,727,632,740,446,499,472,493,753,672,726,699,498,444,719,383,624,491,698,724,464,745,256,695,637,718,382,477,490,440,487,694,741,608,635,716,475,687,380,729,486,692,432,634,739,474,686,712,631,445,471,725,484,376,576,738,671,630,684,497,416,470,443,723,697,623,670,463,717,368,628,680,442,722,468,255,489,622,693,439,381,668,462,715,254,607,438,352,691,620,485,379,714,460,664,633,685,431,711,473,606,252,690,436,378,483,616,456,430,710,683,375,629,737,656,575,604,469,320,482,248,415,669,682,374,428,708,574,627,679,467,441,600,367,414,621,721,667,461,240,372,626,678,424,466,572,366,437,253,619,666,412,459,592,713,663,676,351,224,605,618,568,435,364,251,458,689,408,615,662,377,429,455,350,709,434,250,603,655,360,614,247,560,660,454,427,681,481,373,319,400,192,602,348,707,654,573,246,599,612,413,426,452,318,371,423,677,239,706,625,652,544,344,598,571,365,465,244,411,665,370,422,128,238,591,316,675,570,596,363,648,410,617,336,567,223,457,407,661,590,420,236,674,349,362,312,249,433,566,222,359,406,613,588,659,453,232,559,347,399,601,653,358,245,191,304,564,404,220,425,611,658,346,451,584,558,398,317,343,190,356,651,597,243,610,216,543,421,237,450,369,288,396,556,705,342,315,242,650,409,595,188,569,127,542,647,335,235,419,589,208,314,340,392,552,361,594,311,126,405,334,221,234,184,565,646,418,540,673,587,231,310,357,124,219,332,403,563,644,230,586,303,176,345,536,397,557,308,583,218,355,657,402,189,562,328,302,120,215,228,395,341,582,555,609,354,241,528,160,287,214,187,449,300,649,394,112,541,313,339,554,207,580,286,391,186,212,551,333,233,125,183,296,593,206,338,539,390,309,645,417,284,550,331,96,182,229,123,204,538,175,307,217,388,585,330,535,548,643,280,180,122,227,301,327,401,200,174,119,306,561,64,534,213,642,226,326,581,159,299,353,272,118,172,527,211,185,393,532,285,111,298,158,553,324,205,579,116,295,526,168,210,337,110,181,283,156,389,203,294,549,578,524,95,282,108,179,537,202,329,152,387,279,121,292,173,199,94,547,178,520,305,104,278,386,198,533,225,171,325,63,144,117,546,92,271,157,276,170,297,196,62,115,531,323,167,641,270,88,209,109,525,155,114,60,166,293,530,322,268,107,154,80,281,201,523,151,164,56,291,577,93,106,264,177,103,150,522,277,197,290,91,519,143,48,102,148,169,385,275,195,90,545,142,518,87,61,100,269,274,165,194,113,32,140,59,86,516,153,267,79,321,529,163,58,136,84,105,266,55,149,78,162,263,54,521,101,289,76,262,147,47,89,141,52,46,72,99,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,10 03,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937,936,935,934,933,932,931,930,929,928,927,926,925,924,923,922,921,920,919,918,917,916,915,914,913,912,911,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,862,861,860,859,858,857,856,855,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,839,838,837,836,835,834,833,832,831,830,829,828,827,826,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811,810,809,808,807,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769
M＝960,N＝1024
960,896,959,768,958,956,895,952,512,894,944,892,957,928,955,767,888,954,766,951,880,950,764,893,943,948,864,891,511,942,760,890,927,940,887,510,953,752,926,886,936,765,508,879,949,924,884,763,736,832,878,947,504,920,941,762,863,876,946,759,889,939,862,496,758,912,872,509,938,925,751,885,860,704,935,756,507,923,750,480,883,934,856,831,877,922,506,735,882,748,919,932,503,830,875,640,761,734,848,918,502,744,874,945,828,861,448,871,911,757,732,495,916,500,859,870,910,824,937,703,494,755,728,858,749,855,702,868,754,908,479,933,492,384,816,747,854,921,829,720,505,478,700,881,931,904,746,847,639,733,488,852,827,743,800,917,501,476,930,846,873,696,638,731,826,742,447,256,823,915,499,730,844,869,472,636,446,909,493,727,740,822,688,498,914,857,701,867,815,726,491,840,907,444,632,820,753,464,853,383,719,699,814,672,866,490,724,477,906,487,718,698,382,440,903,745,851,799,812,624,695,475,845,486,637,902,825,716,798,850,741,694,380,474,808,432,843,471,729,635,484,687,608,255,821,796,929,445,692,739,712,900,842,470,376,634,686,725,254,839,819,631,497,443,738,416,792,463,813,671,468,684,913,723,630,838,818,442,252,576,462,368,489,717,439,670,811,697,623,722,784,381,680,628,865,836,905,438,460,715,810,622,797,485,668,693,248,807,379,352,431,473,714,436,849,795,607,901,691,620,483,456,806,711,378,430,664,685,240,375,469,794,633,606,690,482,710,899,791,841,616,804,253,415,428,683,374,320,467,656,629,604,737,790,441,414,708,461,575,367,682,251,669,224,898,372,424,466,837,817,679,627,783,366,574,600,459,412,788,437,250,667,621,678,721,626,247,782,835,809,458,351,364,666,435,572,619,408,455,663,246,592,676,429,192,780,713,350,834,377,434,618,805,605,239,454,360,662,568,615,427,244,793,689,400,348,373,709,603,655,238,803,776,319,614,426,660,452,413,481,423,371,602,789,654,128,560,318,681, 707,344,223,802,236,599,612,411,365,573,422,370,465,787,652,222,249,598,706,316,410,677,363,571,781,544,232,336,407,420,625,591,665,786,457,362,220,596,245,349,570,675,648,897,191,406,359,312,590,779,567,617,433,661,347,243,399,453,674,190,358,216,404,566,778,237,588,346,304,613,398,242,659,775,425,559,451,833,343,188,356,317,601,653,235,564,127,208,658,611,584,396,558,774,342,421,450,234,315,221,288,651,369,597,126,184,231,335,409,610,543,556,340,314,419,392,801,772,219,650,230,334,311,595,124,361,542,569,647,405,176,589,218,418,705,552,310,594,215,332,228,189,357,646,785,540,565,403,120,303,587,214,308,345,397,187,160,355,241,402,328,302,563,673,586,644,207,536,212,777,186,395,583,557,341,112,354,183,562,206,287,300,233,125,394,582,555,339,657,182,286,313,391,773,528,204,333,229,449,296,123,96,554,338,175,541,580,180,609,390,284,217,309,551,331,122,649,227,174,200,771,539,119,550,307,213,330,388,417,280,226,593,159,172,327,301,118,64,538,645,770,306,211,535,548,158,111,185,326,299,205,116,168,401,585,272,210,534,643,110,156,181,298,285,203,561,353,324,527,295,581,108,532,95,393,642,179,202,283,152,294,526,173,199,553,94,337,121,178,579,282,389,104,198,279,171,292,524,549,117,144,92,63,329,578,278,170,387,157,196,225,537,167,115,62,305,271,88,547,520,325,109,155,386,276,166,114,533,209,270,154,60,107,297,546,80,323,151,164,531,106,268,769,93,201,56,293,150,103,322,525,177,281,530,91,143,197,102,291,264,148,48,523,90,142,277,169,641,87,100,61,290,195,522,140,86,275,519,165,59,194,32,577,113,269,153,79,274,518,58,84,163,385,136,55,105,267,78,545,149,162,516,54,266,101,321,76,147,263,529,47,89,141,52,99,46,521,72,262,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998,997,996,995,994,993,992,991,990,989,988,987,986,985,984,983,982,981,980,979,978,977,976,975,974,973,972,971,970,969,968,967,966,965,964,963,962,961
M＝1200,N＝2048
1024,1023,1022,1020,1016,1008,1152,1200,1184,1021,992,1019,1018,1151,1015,960,1014,1150,1199,1007,1012,896,1006,1148,1198,991,1004,1017,990,768,1000,1144,1196,959,1013,988,1183,958,1011,984,1192,1005,512,1136,1010,956,1182,895,976,1003,1149,894,952,989,1002,1180,999,1120,892,1147,987,944,767,998,1197,986,1176,888,957,1146,996,983,766,928,1009,1143,955,982,1195,880,764,975,1142,954,511,980,1088,1001,893,951,974,760,1194,1135,864,510,950,1191,997,1140,891,972,1181,943,985,1168,752,948,1134,890,508,995,968,942,887,832, 1190,765,981,1119,1179,994,927,1132,504,886,940,736,1145,953,979,763,879,926,1188,1118,1178,973,884,936,978,1128,496,762,878,1175,924,949,704,759,971,1141,863,1116,509,876,947,920,1174,758,970,889,1087,480,862,941,967,751,1139,946,507,872,1193,1112,756,640,993,912,966,831,939,860,885,1133,750,1172,1086,506,1138,925,448,964,938,1167,830,503,735,883,856,935,748,977,1104,877,1131,1189,1084,761,923,502,828,734,882,934,1166,744,495,848,922,1117,875,969,1130,703,500,384,932,919,732,757,824,1080,1177,1187,1127,861,494,945,874,1164,918,871,702,965,1115,755,479,728,911,816,1126,859,492,1186,749,870,916,937,700,1173,754,505,963,639,1160,478,910,858,1114,1072,829,256,720,868,855,488,1124,747,1111,800,962,933,881,638,696,908,447,1085,476,1137,501,827,854,733,746,921,1171,1110,847,743,931,446,1056,636,904,826,852,472,688,873,499,731,1083,823,1103,846,742,917,1170,930,493,1108,1165,444,1129,632,498,383,730,701,822,869,1082,844,740,464,1102,727,915,672,815,491,857,1079,753,909,820,382,440,699,1163,914,726,624,867,840,1125,814,477,490,1100,719,961,1078,907,487,853,698,866,380,799,724,1113,745,637,432,812,1162,695,475,718,906,608,1185,255,1071,486,1123,825,798,851,1159,1096,903,1076,376,694,808,474,845,635,741,716,445,929,850,484,254,687,471,902,1109,796,1122,416,729,1070,821,692,1158,634,497,843,576,739,712,443,686,470,368,631,900,252,1055,792,819,1068,842,463,1107,725,738,913,671,1156,442,813,839,630,468,684,1169,1081,489,381,818,1101,439,1054,462,623,248,784,865,670,697,352,723,1106,838,628,1064,811,680,717,905,438,379,622,722,460,485,668,1052,836,797,1099,810,1077,431,693,240,607,473,715,807,436,849,320,378,620,901,456,483,664,1098,430,795,375,1161,691,714,806,1048,606,633,1075,1095,253,711,685,482,415,469,224,616,794,899,374,690,428,841,804,656,791,737,1069,575,1121,604,710,1074,367,1094,414,683,629,441,817,251,467,898,372,1157,790,1040,424,574,461,837,708,669,682,366,600,192,466,783,1067,412,250,627,1092,679,721,788,437,247,572,351,809,621,459,835,782,667,364,1053,1105,626,1155,1066,678,408,592,246,1063,435,458,350,834,666,377,780,619,568,713,128,805,455,676,239,429,663,360,1154,434,1051,244,605,400,793,618,319,689,481,348,1062,454,776,662,238,615,803,427,373,1097,560,709,1050,655,318,603,223,452,1060,344,413,614,802,660,789,426,1047,236,897,681,371,707,654,423,465,602,573,1073,544,316,222,612,365,1093,599,249,411,787,370,706,1046,422,336,652,232,625,677,781,571,598,191,220,410,786,312,1039,363,457,665,420,407,591,1044,1091,648,245,833,570,675,349,779,596,1065,362,190,433,1038,567,216,617,406,590,359,304,674,453,661,778,1090,243,399,347,566,188,775,358,404,127,588,237,1036,208,613,559,242,425,1061,398,659,451,801,288,317,346,774,564,601,653,356,343,126,184,584,658,235,1153,450,558,1049,611,396,369,421,1032,772,705,315,1059,342,221,543,651,234,610,597,124,409,556,335,785,231,176,392,314,419,650,340,542,1058,1045,311,219,569,647,361,334,595,230,552,120,418,405,589,673,540,218,310,160,1 89,594,646,777,332,228,215,1043,357,303,565,403,112,587,308,644,536,241,1037,345,397,187,214,328,402,302,1042,355,563,773,586,657,207,1089,449,583,186,287,557,395,96,212,528,354,300,562,125,341,183,1035,206,233,609,771,582,394,286,555,313,391,649,182,339,296,123,770,204,1034,580,64,541,175,333,284,554,229,417,1031,390,338,551,180,122,593,217,200,309,174,645,119,1057,539,280,331,1030,227,388,550,159,118,172,538,307,330,643,226,401,1028,213,548,272,535,327,111,585,301,158,306,116,642,168,534,326,353,185,561,110,211,1041,156,299,527,205,581,393,95,324,532,210,108,285,298,152,526,181,295,94,203,579,769,553,104,337,283,389,1033,144,524,294,63,202,92,578,179,121,282,199,173,520,292,387,62,549,178,279,88,198,1029,329,386,537,225,117,278,60,171,80,547,196,157,170,115,305,167,109,271,325,155,114,209,276,533,166,546,641,270,107,297,154,323,56,151,531,164,93,106,201,268,525,322,103,293,150,530,177,91,281,48,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,32,59,86,140,113,194,275,518,165,545,79,269,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,2048,2047,2046,2045,2044,2043,2042,2041,2040,2039,2038,2037,2036,2035,2034,2033,2032,2031,2030,2029,2028,2027,2026,2025,2024,2023,2022,2021,2020,2019,2018,2017,2016,2015,2014,2013,2012,2011,2010,2009,2008,2007,2006,2005,2004,2003,2002,2001,2000,1999,1998,1997,1996,1995,1994,1993,1992,1991,1990,1989,1988,1987,1986,1985,1984,1983,1982,1981,1980,1979,1978,1977,1976,1975,1974,1973,1972,1971,1970,1969,1968,1967,1966,1965,1964,1963,1962,1961,1960,1959,1958,1957,1956,1955,1954,1953,1952,1951,1950,1949,1948,1947,1946,1945,1944,1943,1942,1941,1940,1939,1938,1937,1936,1935,1934,1933,1932,1931,1930,1929,1928,1927,1926,1925,1924,1923,1922,1921,1920,1919,1918,1917,1916,1915,1914,1913,1912,1911,1910,1909,1908,1907,1906,1905,1904,1903,1902,1901,1900,1899,1898,1897,1896,1895,1894,1893,1892,1891,1890,1889,1888,1887,1886,1885,1884,1883,1882,1881,1880,1879,1878,1877,1876,1875,1874,1873,1872,1871,1870,1869,1868,1867,1866,1865,1864,1863,1862,1861,1860,1859,1858,1857,1856,1855,1854,1853,1852,1851,1850,1849,1848,1847,1846,1845,1844,1843,1842,1841,1840,1839,1838,1837,1836,1835,1834,1833,1832,1831,1830,1829,1828,1827,1826,1825,1824,1823,1822,1821,1820,1819,1818,1817,1816,1815,1814,1813,1812,1811,1810,1809,1808,1807,1806,1805,1804,1803,1802,1801,1800,1799,1798,1797,1796,1795,1794,1793,1792,1791,1790,1789,1788,1787,1786,1785,1784,1783,1782,1781,1780,1779,1778,1777,1776,1775,1774,1773,1772,1771,1770,1769,1768,1767,1766,1765,1764,1763,1762,1761,1760,1759,1758,1757,1756,1755,1754,175 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M＝1440,N＝2048
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802,1070,897,1165,336,2098,1545,2193,1096,363,1286,220,1123,410,544,1313,191,1170,2064,571,598,652,245,312,2091,2118,407,625,706,787,1055,2145,420,349,2307,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,2077,570,359,665,216,2090,406,596,2185,243,786,1054,2116,433,567,2306,648,1081,2087,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,2075,833,1101,242,2129,404,566,661,1052,2086,346,2181,674,127,1106,208,317,398,588,1077,235,778,1158,343,425,559,1538,2074,1185,356,451,613,775,1099,184,1289,2071,564,659,126,2084,221,288,2179,601,1048,234,315,342,2121,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,2070,801,1069,658,335,2097,2178,1095,124,1285,219,314,409,543,1074,176,1169,340,2063,556,597,651,230,311,2117,392,610,705,772,1040,419,334,2068,1067,1094,361,218,1121,542,1283,189,2062,569,120,650,215,310,2089,405,595,228,785,1053,2115,418,552,2305,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,2060,594,241,308,2114,403,565,646,1051,2085,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,2073,355,212,402,536,183,1050,2056,563,644,125,2083,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,2069,562,657,96,2082,286,2177,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,2067,1093,122,217,284,541,1044,174,338,2061,554,119,649,200,309,390,580,227,770,1038,417,551,2066,1065,331,1091,64,1281,159,539,118,172,213,280,2059,593,226,307,2113,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,2058,116,211,306,401,535,168,1049,2055,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,2054,561,642,95,2081,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,2052,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,2065,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,2057,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,2053,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,2051,106,201,268,525,1028,322,103,293,150,530,177,2050,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,2049,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,4096,4095,4094,4093,4092,4091,4090,4089,4088,4087,4086,4085,4084,4083,4082,4081,4080,4079,4078,4077,4076,4075,4074,4073,4072,4071,4070,4069,4068,4067,4066,4065,4064,4063,4062,4061,4060,4059,4058,4057,4056,4055,4054,4053,4052,4051,4050,4049,4048,4047,4046,4045,4044,4043,4042,404 1,4040,4039,4038,4037,4036,4035,4034,4033,4032,4031,4030,4029,4028,4027,4026,4025,4024,4023,4022,4021,4020,4019,4018,4017,4016,4015,4014,4013,4012,4011,4010,4009,4008,4007,4006,4005,4004,4003,4002,4001,4000,3999,3998,3997,3996,3995,3994,3993,3992,3991,3990,3989,3988,3987,3986,3985,3984,3983,3982,3981,3980,3979,3978,3977,3976,3975,3974,3973,3972,3971,3970,3969,3968,3967,3966,3965,3964,3963,3962,3961,3960,3959,3958,3957,3956,3955,3954,3953,3952,3951,3950,3949,3948,3947,3946,3945,3944,3943,3942,3941,3940,3939,3938,3937,3936,3935,3934,3933,3932,3931,3930,3929,3928,3927,3926,3925,3924,3923,3922,3921,3920,3919,3918,3917,3916,3915,3914,3913,3912,3911,3910,3909,3908,3907,3906,3905,3904,3903,3902,3901,3900,3899,3898,3897,3896,3895,3894,3893,3892,3891,3890,3889,3888,3887,3886,3885,3884,3883,3882,3881,3880,3879,3878,3877,3876,3875,3874,3873,3872,3871,3870,3869,3868,3867,3866,3865,3864,3863,3862,3861,3860,3859,3858,3857,3856,3855,3854,3853,3852,3851,3850,3849,3848,3847,3846,3845,3844,3843,3842,3841,3840,3839,3838,3837,3836,3835,3834,3833,3832,3831,3830,3829,3828,3827,3826,3825,3824,3823,3822,3821,3820,3819,3818,3817,3816,3815,3814,3813,3812,3811,3810,3809,3808,3807,3806,3805,3804,3803,3802,3801,3800,3799,3798,3797,3796,3795,3794,3793,3792,3791,3790,3789,3788,3787,3786,3785,3784,3783,3782,3781,3780,3779,3778,3777,3776,3775,3774,3773,3772,3771,3770,3769,3768,3767,3766,3765,3764,3763,3762,3761,3760,3759,3758,3757,3756,3755,3754,3753,3752,3751,3750,3749,3748,3747,3746,3745,3744,3743,3742,3741,3740,3739,3738,3737,3736,3735,3734,3733,3732,3731,3730,3729,3728,3727,3726,3725,3724,3723,3722,3721,3720,3719,3718,3717,3716,3715,3714,3713,3712,3711,3710,3709,3708,3707,3706,3705,3704,3703,3702,3701,3700,3699,3698,3697,3696,3695,3694,3693,3692,3691,3690,3689,3688,3687,3686,3685,3684,3683,3682,3681,3680,3679,3678,3677,3676,3675,3674,3673,3672,3671,3670,3669,3668,3667,3666,3665,3664,3663,3662,3661,3660,3659,3658,3657,3656,3655,3654,3653,3652,3651,3650,3649,3648,3647,3646,3645,3644,3643,3642,3641,3640,3639,3638,3637,3636,3635,3634,3633,3632,3631,3630,3629,3628,3627,3626,3625,3624,3623,3622,3621,3620,3619,3618,3617,3616,3615,3614,3613,3612,3611,3610,3609,3608,3607,3606,3605,3604,3603,3602,3601,3600,3599,3598,3597,3596,3595,3594,3593,3592,3591,3590,3589,3588,3587,3586,3585,3584,3583,3582,3581,3580,3579,3578,3577,3576,3575,3574,3573,3572,3571,3570,3569,3568,3567,3566,3565,3564,3563,3562,3561,3560,3559,3558,3557,3556,3555,3554,3553,3552,3551,3550,3549,3548,3547,3546,3545,3544,3543,3542,3541,3540,3539,3538,3537,3536,3535,3534,3533,3532,3531,3530,3529,3528,3527,3526,3525,3524,3523,3522,3521,3520,3519,3518,3517,3516,3515,3514,3513,3512,3511,3510,3509,3508,3507,3506,3505,3504,3503,3502,3501,3500,3499,3498,3497,3496,3495,3494,3493,3492,3491,3490,3489,3488,3487,3486,3485,3484,3483,3482,3481,3480,3479,3478,3477,3476,3475,3474,3473,3472,3471,3470,3469,3468,3467,3466,3465,3464,3463,3462,3461,3460,3459,3458,3457,345 6,3455,3454,3453,3452,3451,3450,3449,3448,3447,3446,3445,3444,3443,3442,3441,3440,3439,3438,3437,3436,3435,3434,3433,3432,3431,3430,3429,3428,3427,3426,3425,3424,3423,3422,3421,3420,3419,3418,3417,3416,3415,3414,3413,3412,3411,3410,3409,3408,3407,3406,3405,3404,3403,3402,3401,3400,3399,3398,3397,3396,3395,3394,3393,3392,3391,3390,3389,3388,3387,3386,3385,3384,3383,3382,3381,3380,3379,3378,3377,3376,3375,3374,3373,3372,3371,3370,3369,3368,3367,3366,3365,3364,3363,3362,3361,3360,3359,3358,3357,3356,3355,3354,3353,3352,3351,3350,3349,3348,3347,3346,3345,3344,3343,3342,3341,3340,3339,3338,3337,3336,3335,3334,3333,3332,3331,3330,3329,3328,3327,3326,3325,3324,3323,3322,3321,3320,3319,3318,3317,3316,3315,3314,3313,3312,3311,3310,3309,3308,3307,3306,3305,3304,3303,3302,3301,3300,3299,3298,3297,3296,3295,3294,3293,3292,3291,3290,3289,3288,3287,3286,3285,3284,3283,3282,3281,3280,3279,3278,3277,3276,3275,3274,3273,3272,3271,3270,3269,3268,3267,3266,3265,3264,3263,3262,3261,3260,3259,3258,3257,3256,3255,3254,3253,3252,3251,3250,3249,3248,3247,3246,3245,3244,3243,3242,3241,3240,3239,3238,3237,3236,3235,3234,3233,3232,3231,3230,3229,3228,3227,3226,3225,3224,3223,3222,3221,3220,3219,3218,3217,3216,3215,3214,3213,3212,3211,3210,3209,3208,3207,3206,3205,3204,3203,3202,3201,3200,3199,3198,3197,3196,3195,3194,3193,3192,3191,3190,3189,3188,3187,3186,3185,3184,3183,3182,3181,3180,3179,3178,3177,3176,3175,3174,3173,3172,3171,3170,3169,3168,3167,3166,3165,3164,3163,3162,3161,3160,3159,3158,3157,3156,3155,3154,3153,3152,3151,3150,3149,3148,3147,3146,3145,3144,3143,3142,3141,3140,3139,3138,3137,3136,3135,3134,3133,3132,3131,3130,3129,3128,3127,3126,3125,3124,3123,3122,3121,3120,3119,3118,3117,3116,3115,3114,3113,3112,3111,3110,3109,3108,3107,3106,3105,3104,3103,3102,3101,3100,3099,3098,3097,3096,3095,3094,3093,3092,3091,3090,3089,3088,3087,3086,3085,3084,3083,3082,3081,3080,3079,3078,3077,3076,3075,3074,3073,3072,3071,3070,3069,3068,3067,3066,3065,3064,3063,3062,3061,3060,3059,3058,3057,3056,3055,3054,3053,3052,3051,3050,3049,3048,3047,3046,3045,3044,3043,3042,3041,3040,3039,3038,3037,3036,3035,3034,3033,3032,3031,3030,3029,3028,3027,3026,3025,3024,3023,3022,3021,3020,3019,3018,3017,3016,3015,3014,3013,3012,3011,3010,3009,3008,3007,3006,3005,3004,3003,3002,3001,3000,2999,2998,2997,2996,2995,2994,2993,2992,2991,2990,2989,2988,2987,2986,2985,2984,2983,2982,2981,2980,2979,2978,2977,2976,2975,2974,2973,2972,2971,2970,2969,2968,2967,2966,2965,2964,2963,2962,2961,2960,2959,2958,2957,2956,2955,2954,2953,2952,2951,2950,2949,2948,2947,2946,2945,2944,2943,2942,2941,2940,2939,2938,2937,2936,2935,2934,2933,2932,2931,2930,2929,2928,2927,2926,2925,2924,2923,2922,2921,2920,2919,2918,2917,2916,2915,2914,2913,2912,2911,2910,2909,2908,2907,2906,2905,2904,2903,2902,2901,2900,2899,2898,2897,2896,2895,2894,2893,2892,2891,2890,2889,2888,2887,2886,2885,2884,2883,2882,2881,2880,2879,2878,2877,2876,2875,2874,2873,2872,287 1,2870,2869,2868,2867,2866,2865,2864,2863,2862,2861,2860,2859,2858,2857,2856,2855,2854,2853,2852,2851,2850,2849,2848,2847,2846,2845,2844,2843,2842,2841,2840,2839,2838,2837,2836,2835,2834,2833,2832,2831,2830,2829,2828,2827,2826,2825,2824,2823,2822,2821,2820,2819,2818,2817,2816,2815,2814,2813,2812,2811,2810,2809,2808,2807,2806,2805,2804,2803,2802,2801,2800,2799,2798,2797,2796,2795,2794,2793,2792,2791,2790,2789,2788,2787,2786,2785,2784,2783,2782,2781,2780,2779,2778,2777,2776,2775,2774,2773,2772,2771,2770,2769,2768,2767,2766,2765,2764,2763,2762,2761,2760,2759,2758,2757,2756,2755,2754,2753,2752,2751,2750,2749,2748,2747,2746,2745,2744,2743,2742,2741,2740,2739,2738,2737,2736,2735,2734,2733,2732,2731,2730,2729,2728,2727,2726,2725,2724,2723,2722,2721,2720,2719,2718,2717,2716,2715,2714,2713,2712,2711,2710,2709,2708,2707,2706,2705,2704,2703,2702,2701,2700,2699,2698,2697,2696,2695,2694,2693,2692,2691,2690,2689,2688,2687,2686,2685,2684,2683,2682,2681,2680,2679,2678,2677,2676,2675,2674,2673,2672,2671,2670,2669,2668,2667,2666,2665,2664,2663,2662,2661,2660,2659,2658,2657,2656,2655,2654,2653,2652,2651,2650,2649,2648,2647,2646,2645,2644,2643,2642,2641,2640,2639,2638,2637,2636,2635,2634,2633,2632,2631,2630,2629,2628,2627,2626,2625,2624,2623,2622,2621,2620,2619,2618,2617,2616,2615,2614,2613,2612,2611,2610,2609,2608,2607,2606,2605,2604,2603,2602,2601,2600,2599,2598,2597,2596,2595,2594,2593,2592,2591,2590,2589,2588,2587,2586,2585,2584,2583,2582,2581,2580,2579,2578,2577,2576,2575,2574,2573,2572,2571,2570,2569,2568,2567,2566,2565,2564,2563,2562,2561,2560,2559,2558,2557,2556,2555,2554,2553,2552,2551,2550,2549,2548,2547,2546,2545,2544,2543,2542,2541,2540,2539,2538,2537,2536,2535,2534,2533,2532,2531,2530,2529,2528,2527,2526,2525,2524,2523,2522,2521,2520,2519,2518,2517,2516,2515,2514,2513,2512,2511,2510,2509,2508,2507,2506,2505,2504,2503,2502,2501,2500,2499,2498,2497,2496,2495,2494,2493,2492,2491,2490,2489,2488,2487,2486,2485,2484,2483,2482,2481,2480,2479,2478,2477,2476,2475,2474,2473,2472,2471,2470,2469,2468,2467,2466,2465,2464,2463,2462,2461,2460,2459,2458,2457,2456,2455,2454,2453,2452,2451,2450,2449,2448,2447,2446,2445,2444,2443,2442,2441,2440,2439,2438,2437,2436,2435,2434,2433,2432,2431,2430,2429,2428,2427,2426,2425,2424,2423,2422,2421,2420,2419,2418,2417,2416,2415,2414,2413,2412,2411,2410,2409,2408,2407,2406,2405,2404,2403,2402,2401
表4
M＝48,N＝64
63,62,61,59,58,55,54,47,46,31,30,57,53,51,50,45,43,42,39,29,27,38,26,23,22,15,14,49,41,37,25,35,21,34,19,13,18,11,10,7,6,33,17,9,5,3,2,1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64
M＝72,N＝128
127,125,123,119,111,95,63,121,114,117,115,109,107,93,103,91,61,87,59,113,79,55,105,47,101,89,99,31,85,98,57,83,77,82,53,75,51,45,71,50,43,97,29,39,27,81,23,73,49,15,69,41,67,66,37,25,35,21,34,19,13,18,11,65,7,33,17,9,5,3,2,1,4,6,8,10,12,14,16,20,22,24,26,28,30,32,36,38,40,42,44,46,48,52,54,56,58,60,62,64,68,70,72,74,76,78,80,84,86,88,90,92,94,96,100,102,104,106,108,110,112,116,118,120,122,124,126,128
M＝96,N＝128
127,126,125,123,122,119,118,111,110,95,94,63,121,62,117,115,114,109,107,106,103,93,91,102,90,87,86,61,59,79,58,78,55,54,113,47,46,105,101,31,99,89,30,98,85,83,82,57,77,75,53,51,74,71,50,45,70,43,42,39,97,29,27,81,38,26,23,73,22,49,15,69,14,41,67,66,37,25,35,21,34,19,13,18,11,65,10,7,6,33,17,9,5,3,2,1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128
M＝120,N＝128
127,126,124,120,125,123,122,119,111,118,110,116,95,108,94,104,121,63,92,117,62,88,115,109,60,114,107,56,106,93,103,91,102,90,61,87,100,79,86,59,113,78,58,84,55,105,47,76,54,101,46,52,72,89,31,99,44,85,30,98,83,40,77,57,28,82,75,53,24,74,51,45,71,50,43,70,42,29,68,39,97,27,38,26,81,23,36,15,22,73,14,20,49,69,41,12,67,37,66,25,8,35,21,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,16,32,48,64,80,96,112,128
M＝144,N＝256
223,239,191,247,251,127,253,255,249,242,245,243,237,235,231,221,219,215,189,187,241,207,183,125,233,123,175,229,217,119,227,159,213,226,111,185,211,205,210,181,95,203,179,121,173,199,178,63,117,171,225,157,115,167,109,155,114,209,107,151,93,201,103,177,91,143,197,61,87,169,195,59,113,194,165,79,153,55,163,105,149,162,47,101,147,89,141,99,146,31,85,139,98,193,57,83,135,77,82,53,161,75,51,45,71,50,145,43,97,29,137,39,27,81,133,23,131,73,49,130,15,69,41,67,66,37,25,35,21,34,129,19,13,18,11,65,7,33,17,9,5,3,2,1,4,6,8,10,12,14,16,20,22,24,26,28,30,32,36,38,40,42,44,46,48,52,54,56,58,60,62,64,68,70,72,74,76,78,80,84,86,88,90,92,94,96,100,102,104,106,108,110,112,116,118,120,122,124,126,128,132,134,136,138,140,142,144,148,150,152,154,156,158,160,164,166,168,170,172,174,176,180,182,184,186,188,190,192,196,198,200,202,204,206,208,212,214,216,218,220,222,224,228,230,232,234,236,238,240,244,246,248,250,252,254,256
M＝160,N＝256
247,250,251,239,253,255,223,191,127,249,245,242,243,237,234,235,231,221,218,219,215,189,207,186,187,183,175,125,122,123,119,159,111,241,233,95,229,226,227,217,213,210,211,205,185,202,203,181,179,121,173,199,178,63,117,171,225,157,170,115,167,109,155,114,209,107,154,151,93,106,201,103,177,91,143,197,90,61,87,169,195,59,113,194,165,79,58,153,55,163,105,149,162,47,101,147,89,141,99,146,31,85,139,98,193,57,138,83,135,77,82,53,161,75,51,74,45,71,50,145,43,97,29,42,137,39,27,81,133,26,23,131,73,49,130,15,69,41,67,66,37,25,35,21,34,129,19,13,18,11,65,10,7,33,17,9,5,3,2,1,4,6,8,12,14,16,20,22,24,28,30,32,36,38,40,44,46,48,52,54,56,60,62,64,68,70,72,76,78,80,84,86,88,92,94,96,100,102,104,108,110,112,116,118,120,124,126,128,132,134,136,140,142,144,148,150,152,156,158,160,164,166,168,172,174,176,180,182,184,188,190,192,196,198,200,204,206,208,212,214,216,220,222,224,228,230,232,236,238,240,244,246,248,252,254,256
M＝180,N＝256
255,253,250,251,247,246,239,223,191,249,245,127,243,242,237,234,235,231,230,221,218,219,215,214,189,206,186,187,207,183,182,175,125,122,123,119,118,241,159,233,111,229,227,217,226,213,211,95,210,205,185,203,202,181,179,199,178,173,198,63,170,171,121,167,166,157,117,115,154,155,114,109,106,107,151,150,103,102,93,142,143,90,91,87,86,61,78,58,225,209,201,177,197,169,195,59,113,194,165,79,153,55,163,105,54,149,162,47,101,147,89,141,99,146,31,85,139,98,193,57,138,83,135,77,82,53,134,161,75,51,74,45,71,50,145,43,70,97,29,42,137,39,27,81,38,133,26,23,131,73,22,49,130,15,69,14,41,67,66,37,25,35,21,34,129,19,13,18,11,65,10,7,6,33,17,9,5,3,2,1,4,8,12,16,20,24,28,30,32,36,40,44,46,48,52,56,60,62,64,68,72,76,80,84,88,92,94,96,100,104,108,110,112,116,120,124,126,128,132,136,140,144,148,152,156,158,160,164,168,172,174,176,180,184,188,190,192,196,200,204,208,212,216,220,222,224,228,232,236,238,240,244,248,252,254,256
M＝192,N＝256
254,255,253,251,250,247,246,239,238,223,222,191,190,249,245,243,127,242,126,237,235,234,231,221,230,219,218,215,214,189,187,207,186,206,183,182,175,125,123,174,241,122,119,233,159,118,229,158,227,111,217,110,226,213,211,210,95,205,185,203,94,181,179,202,199,178,173,63,198,171,62,121,170,167,117,115,157,155,166,114,154,109,107,151,106,150,103,93,91,143,102,225,90,142,87,86,209,61,59,79,201,58,78,55,177,197,54,195,47,169,194,46,165,163,153,113,105,149,162,101,147,89,141,99,146,31,85,139,98,193,30,57,138,83,135,77,82,53,134,161,75,51,74,45,71,50,145,43,70,97,29,42,137,39,27,81,38,133,26,23,13 1,73,22,49,130,15,69,14,41,67,66,37,25,35,21,34,129,19,13,18,11,65,10,7,6,33,17,9,5,3,2,1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,156,160,164,168,172,176,180,184,188,192,196,200,204,208,212,216,220,224,228,232,236,240,244,248,252,256
M＝240,N＝256
255,254,252,248,253,251,250,247,246,239,244,238,223,236,222,232,220,191,249,190,245,216,243,237,188,127,242,235,126,184,234,221,231,124,219,230,218,215,189,228,120,207,214,187,206,186,212,241,183,125,204,175,182,233,123,174,229,180,200,122,217,159,119,227,172,213,118,111,158,226,211,168,110,116,205,185,156,210,95,203,108,181,152,94,202,179,173,199,104,121,178,63,92,171,198,117,62,170,157,196,88,167,115,109,155,225,60,166,114,154,107,151,164,209,56,106,93,143,150,103,201,91,102,142,148,177,90,197,87,61,100,140,169,79,86,195,59,165,78,194,58,84,136,113,153,55,163,76,47,54,105,149,162,46,101,52,147,72,141,89,31,99,44,146,139,85,30,98,138,40,83,135,77,28,57,82,134,75,53,24,74,193,51,132,45,71,50,43,70,161,42,29,145,68,39,27,97,137,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256
M＝288,N＝512
383,255,447,443,445,439,463,431,471,381,379,475,477,375,415,367,479,487,491,493,495,498,499,501,351,511,509,507,503,505,497,489,485,473,483,253,469,482,251,441,467,461,466,247,437,459,435,377,239,429,455,434,319,373,427,481,223,413,371,423,365,249,411,370,465,363,191,245,407,349,457,359,243,433,347,237,399,453,242,127,317,235,343,425,451,221,315,369,450,231,421,335,219,409,311,419,361,189,215,405,418,303,357,187,241,403,345,207,397,355,402,183,125,287,233,341,395,354,449,123,313,175,339,229,391,333,217,338,119,309,227,417,331,159,213,226,307,111,301,327,185,211,306,401,205,299,353,210,181,95,285,203,393,295,179,121,283,173,337,199,389,178,63,117,171,279,225,387,329,157,115,305,386,167,109,271,325,155,114,209,107,297,323,151,93,201,322,103,293,177,91,281,143,197,291,61,87,169,277,195,290,385,59,113,194,275,165,79,269,153,274,55,163,105,267,321,149,162,47,101,263,147,89,141,99,289,146,31,85,139,98,193,57,83,273,135,77,82,53,161,75,265,51,45,71,261,50,145,43,97,259,29,137,258,39,27,81,133,23,131,73,49,130,15,69,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,7,33,17,9,5,3,2,1,4,6,8,10,12,14,16,20,22,24,26,28,30,32,36,38,40,42,44,46,48,52,54,56,58,60,62,64,68,70,72,74,76,78,80,84,86,88,90,92,94,96,100,102,104,106,108,110,112,116,118,120,122,124,126,128,132 ,134,136,138,140,142,144,148,150,152,154,156,158,160,164,166,168,170,172,174,176,180,182,184,186,188,190,192,196,198,200,202,204,206,208,212,214,216,218,220,222,224,228,230,232,234,236,238,240,244,246,248,250,252,254,256,260,262,264,266,268,270,272,276,278,280,282,284,286,288,292,294,296,298,300,302,304,308,310,312,314,316,318,320,324,326,328,330,332,334,336,340,342,344,346,348,350,352,356,358,360,362,364,366,368,372,374,376,378,380,382,384,388,390,392,394,396,398,400,404,406,408,410,412,414,416,420,422,424,426,428,430,432,436,438,440,442,444,446,448,452,454,456,458,460,462,464,468,470,472,474,476,478,480,484,486,488,490,492,494,496,500,502,504,506,508,510,512
M＝300,N＝512
383,255,447,471,475,445,463,477,443,479,439,487,491,431,493,495,379,381,415,375,498,499,501,367,503,505,507,351,253,509,251,247,511,239,319,497,223,489,482,485,473,483,466,469,458,467,461,441,191,459,434,437,435,377,429,455,373,427,481,413,426,371,423,365,249,411,370,465,363,245,407,349,457,359,243,433,347,237,399,453,242,127,317,235,343,425,451,221,315,369,450,231,421,335,219,409,311,419,361,189,215,405,418,303,357,187,241,403,345,207,397,355,402,183,125,287,233,341,395,354,449,123,313,394,175,339,229,391,333,217,338,119,309,227,417,331,159,213,226,307,330,111,301,327,185,211,306,401,205,299,353,210,181,95,285,203,298,393,295,179,121,202,283,173,337,199,389,178,63,117,171,279,225,387,329,157,170,115,305,386,167,109,271,325,155,114,209,107,297,323,151,93,201,322,103,293,177,91,281,143,197,291,61,87,169,277,195,290,385,59,113,194,275,165,79,269,153,274,55,163,105,267,321,149,162,266,47,101,263,147,89,141,99,289,146,31,85,139,98,193,57,138,83,273,135,77,82,53,161,75,265,51,74,45,71,261,50,145,43,97,259,29,42,137,258,39,27,81,133,23,131,73,49,130,15,69,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,10,7,33,17,9,5,3,2,1,4,6,8,12,14,16,20,22,24,26,28,30,32,36,38,40,44,46,48,52,54,56,58,60,62,64,68,70,72,76,78,80,84,86,88,90,92,94,96,100,102,104,106,108,110,112,116,118,120,122,124,126,128,132,134,136,140,142,144,148,150,152,154,156,158,160,164,166,168,172,174,176,180,182,184,186,188,190,192,196,198,200,204,206,208,212,214,216,218,220,222,224,228,230,232,234,236,238,240,244,246,248,250,252,254,256,260,262,264,268,270,272,276,278,280,282,284,286,288,292,294,296,300,302,304,308,310,312,314,316,318,320,324,326,328,332,334,336,340,342,344,346,348,350,352,356,358,360,362,364,366,368,372,374,376,378,380,382,384,388,390,392,396,398,400,404,406,408,410,412,414,416,420,422,424,428,430,432,436,438,440,442,444,446,448,452,454,456,460,462,464,468,470,472,474,476,478,480,484,486,488,490,492,494,496,500,502,504,506,508,510,512
M＝360,N＝512
479,447,495,502,503,506,507,509,511,383,505,501,499,498,493,490,491,487,255,486,477,474,475,471,470,462,445,463,442,443,439,438,431,381,378,379,375,374,415,367,497,253,489,250,251,351,485,247,246,483,473,482,469,467,239,466,461,441,459,319,458,437,435,455,434,429,454,223,426,427,377,423,422,413,373,410,411,371,370,365,191,407,362,363,406,359,358,349,398,399,346,347,249,245,343,243,342,127,242,237,317,234,235,334,314,315,335,231,230,221,311,310,481,218,219,465,457,214,215,303,433,189,453,206,451,425,186,187,207,450,421,183,182,287,419,409,369,418,175,405,125,361,403,122,123,402,357,397,119,118,355,345,395,159,354,394,341,339,391,111,241,338,390,333,233,313,331,330,229,309,307,227,449,217,417,213,226,301,327,185,211,306,401,205,299,326,353,210,181,95,285,203,298,393,295,179,121,202,283,173,337,199,294,389,178,282,63,117,171,198,279,225,387,329,157,170,278,115,305,386,167,109,271,325,155,114,209,166,270,107,297,154,323,151,93,106,201,322,103,293,150,177,91,281,143,102,197,291,90,61,142,87,169,277,195,290,385,59,86,113,194,275,165,79,269,58,153,274,55,163,78,105,267,321,54,149,162,266,47,101,263,147,89,141,262,99,289,146,31,85,139,98,193,57,138,83,273,135,77,82,53,134,161,75,265,51,74,45,71,261,50,145,43,70,97,259,29,42,137,258,39,27,81,38,133,26,23,131,73,22,49,130,15,69,14,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,10,7,6,33,17,9,5,3,2,1,4,8,12,16,20,24,28,30,32,36,40,44,46,48,52,56,60,62,64,68,72,76,80,84,88,92,94,96,100,104,108,110,112,116,120,124,126,128,132,136,140,144,148,152,156,158,160,164,168,172,174,176,180,184,188,190,192,196,200,204,208,212,216,220,222,224,228,232,236,238,240,244,248,252,254,256,260,264,268,272,276,280,284,286,288,292,296,300,302,304,308,312,316,318,320,324,328,332,336,340,344,348,350,352,356,360,364,366,368,372,376,380,382,384,388,392,396,400,404,408,412,414,416,420,424,428,430,432,436,440,444,446,448,452,456,460,464,468,472,476,478,480,484,488,492,494,496,500,504,508,510,512
M＝384,N＝512
495,494,502,503,506,507,509,510,479,478,511,447,446,383,382,505,501,499,498,493,491,490,487,486,477,475,255,474,254,471,470,445,463,443,462,442,439,438,431,430,381,379,378,375,415,374,414,367,497,366,489,253,251,485,483,473,250,351,482,247,350,469,467,246,466,461,441,239,459,238,437,458,435,319,455,318,434,429,454,427,223,426,222,377,423,373,413,371,422,411,370,410,365,363,407,191,362,406,190,359,349,249,399,358,347,245,398,346,243,343,242,127,342,237,235,481,126,317,315,234,335,465,231,314,334,221,311,230,219,457,310,218,433,215,453,451,303,425,214,450,302,189,187,421,207,419,409,186,369,206,183,287,418,405,182,361,403,286,357,402,355,175,125,397,123,174,345,395,354,122,341,119,394,339,241,391,159,118,338,233,333,158,390,111,313,331,229,110,309,227,330,307,217,327,226,306,213,301,95,326,211,299,94,298,210,205 ,185,295,203,285,181,294,283,202,179,199,449,417,401,353,393,121,173,337,389,178,282,63,117,171,198,279,225,387,329,62,157,170,278,115,305,386,167,109,271,325,155,114,209,166,270,107,297,154,323,151,93,106,201,322,103,293,150,177,91,281,143,102,197,291,90,61,142,87,169,277,195,290,385,59,86,113,194,275,165,79,269,58,153,274,55,163,78,105,267,321,54,149,162,266,47,101,263,147,89,46,141,262,99,289,146,31,85,139,98,193,30,57,138,83,273,135,77,82,53,134,161,75,265,51,74,45,71,261,50,145,43,70,97,259,29,42,137,258,39,27,81,38,133,26,23,131,73,22,49,130,15,69,14,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,10,7,6,33,17,9,5,3,2,1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,156,160,164,168,172,176,180,184,188,192,196,200,204,208,212,216,220,224,228,232,236,240,244,248,252,256,260,264,268,272,276,280,284,288,292,296,300,304,308,312,316,320,324,328,332,336,340,344,348,352,356,360,364,368,372,376,380,384,388,392,396,400,404,408,412,416,420,424,428,432,436,440,444,448,452,456,460,464,468,472,476,480,484,488,492,496,500,504,508,512
M＝400,N＝512
510,509,507,511,506,503,502,495,494,479,478,447,446,383,382,505,501,499,498,493,491,490,487,484,477,486,475,474,255,471,254,470,445,463,443,462,442,439,438,431,430,381,379,378,375,415,374,414,497,367,489,366,485,483,253,251,473,482,250,469,351,467,247,350,246,466,461,441,459,239,437,458,435,238,455,319,434,452,429,454,427,318,223,426,377,423,222,373,420,413,371,422,411,370,410,365,363,407,191,362,406,359,190,249,349,356,347,399,358,245,243,398,346,343,481,242,237,127,342,235,465,317,126,315,234,335,231,457,314,334,221,228,311,219,230,433,453,310,451,218,425,215,303,450,421,214,419,189,302,187,409,369,207,418,186,405,361,183,206,287,403,182,357,286,402,355,397,345,395,175,125,123,354,341,174,394,339,241,122,391,119,338,233,388,333,313,390,118,159,331,158,229,309,111,330,307,227,217,110,327,306,226,213,324,301,211,326,299,95,210,298,205,185,94,203,295,285,292,181,294,283,202,179,199,282,178,63,196,173,279,198,171,62,278,449,170,121,167,417,117,271,115,164,157,155,166,401,270,114,154,109,107,353,393,337,389,225,387,329,305,386,325,209,297,323,151,93,106,201,322,103,293,150,177,91,281,143,102,197,291,90,61,142,87,169,277,100,195,290,385,59,86,113,194,275,165,79,269,58,153,274,55,163,78,105,267,321,54,149,162,266,47,101,263,147,89,46,141,262,99,289,146,31,85,139,98,193,260,30,57,138,83,273,135,77,82,53,134,161,75,265,51,132,74,45,71,261,50,145,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,14,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,8,12,16,20,24,28,32,40,44,48,52,56,60,64,72,76,80,84,88,92,96,104,108,112,116,120,124,128,136,140,144,148,152,156,160,168,172,176,18 0,184,188,192,200,204,208,212,216,220,224,232,236,240,244,248,252,256,264,268,272,276,280,284,288,296,300,304,308,312,316,320,328,332,336,340,344,348,352,360,364,368,372,376,380,384,392,396,400,404,408,412,416,424,428,432,436,440,444,448,456,460,464,468,472,476,480,488,492,496,500,504,508,512
M＝480,N＝512
511,510,508,504,509,507,506,503,502,495,500,494,492,479,478,488,476,447,505,446,472,501,444,499,493,383,498,491,440,382,490,477,487,380,475,486,255,474,471,484,376,254,445,470,463,443,252,468,462,442,439,497,460,438,248,381,431,489,379,430,436,456,485,378,375,415,428,473,483,374,414,367,253,469,482,424,366,372,251,467,412,461,441,250,466,351,364,459,247,437,408,350,458,246,435,239,429,360,455,434,348,319,377,238,244,427,454,318,373,426,223,413,236,344,452,423,371,222,365,411,316,422,370,481,232,410,363,220,249,191,407,420,312,362,465,349,406,399,359,190,245,216,347,457,358,398,243,404,237,188,346,127,433,242,343,453,356,317,235,396,425,126,342,335,184,315,234,451,221,231,421,334,314,340,392,124,450,219,311,230,369,409,419,218,332,310,303,361,215,228,405,189,120,418,302,214,308,207,357,187,403,328,397,345,287,206,186,212,300,355,402,395,183,241,341,286,125,354,204,182,175,394,233,296,339,391,333,123,284,313,174,180,229,338,200,122,390,331,309,217,159,119,172,227,280,330,449,307,118,111,158,388,213,301,327,226,306,168,110,211,116,299,326,205,156,185,417,210,95,298,285,108,203,181,324,295,401,152,94,283,202,179,294,173,353,199,104,282,393,178,92,121,63,171,198,279,292,337,62,117,170,278,389,271,157,88,196,167,115,329,109,155,270,60,276,387,166,114,225,154,305,107,325,386,151,268,164,56,106,93,297,209,150,143,103,323,91,102,264,201,293,142,148,322,90,281,177,87,100,291,197,61,140,277,86,169,79,59,290,195,78,275,84,58,136,165,269,55,194,153,113,274,76,163,54,47,267,105,149,162,266,46,52,72,147,101,263,141,44,31,89,146,99,262,139,30,385,85,98,40,138,260,28,83,77,135,57,82,134,75,24,53,321,74,51,289,132,45,71,193,50,273,161,265,261,145,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,304,320,336,352,368,384,400,416,432,448,464,480,496,512
M＝576,N＝1024
511,759,763,765,767,751,735,509,831,507,503,703,495,863,879,479,887,891,893,889,895,1023,1021,1019,1015,1007,991,1017,959,1013,1011,1005,1010,1003,989,999,987,957,983,955,1009,975,951,1001,943,997,985,995,927,981,994,953,979,973,978,949,971,947,941,967,946,885,939,993,925,883,935,877,761,923,882,977,875,757,919,861,969,871,755,945,859,749,911,965,754,505,639,829,747,85 5,937,963,733,447,827,501,881,962,743,933,847,731,921,499,823,931,493,873,701,498,727,917,930,383,491,815,869,699,753,915,477,857,719,909,487,867,914,695,475,637,799,745,853,907,866,961,255,445,635,825,471,687,851,741,903,845,729,443,850,497,631,821,739,929,463,843,671,725,439,738,819,381,489,623,813,839,697,723,818,913,379,717,431,811,485,865,722,693,473,607,797,715,375,905,483,807,691,253,415,633,795,469,685,849,482,711,901,690,367,251,441,575,467,629,683,791,737,899,461,841,669,466,247,437,627,817,898,351,679,459,621,783,837,667,626,721,435,377,239,429,619,809,455,835,434,663,605,319,713,373,427,834,481,615,805,689,223,413,603,793,655,371,709,423,803,365,249,411,573,370,465,599,681,789,707,802,897,363,191,571,245,407,625,706,787,349,677,457,591,781,359,665,243,786,433,567,347,675,237,399,617,779,453,833,242,661,674,127,317,235,343,425,559,451,613,775,659,221,601,315,653,369,450,231,421,611,801,658,335,219,409,543,597,651,311,610,705,419,361,189,569,215,405,595,785,418,647,589,303,357,187,594,241,403,565,345,673,207,397,587,777,355,402,183,563,125,287,233,341,395,557,354,449,583,773,562,657,123,313,175,339,555,229,391,609,771,333,217,541,338,119,649,309,227,770,417,551,331,159,539,213,593,226,307,645,111,301,327,185,211,306,401,535,643,205,585,299,353,210,181,561,642,95,285,203,393,527,581,295,179,121,283,173,337,553,199,389,579,769,178,63,117,171,279,578,225,387,549,329,157,537,115,305,386,167,547,109,271,325,155,114,209,533,546,641,107,297,323,151,531,93,201,525,322,103,293,530,177,91,281,143,523,197,577,291,61,87,169,277,195,290,385,519,59,113,194,275,165,545,79,269,153,274,55,163,105,267,321,149,529,162,47,101,263,147,89,141,521,99,289,146,31,85,139,98,193,517,57,83,273,135,515,77,82,53,514,161,75,265,51,45,71,261,50,145,43,97,259,29,137,258,39,27,81,133,513,23,131,73,49,130,15,69,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,7,33,17,9,5,3,2,1,4,6,8,10,12,14,16,20,22,24,26,28,30,32,36,38,40,42,44,46,48,52,54,56,58,60,62,64,68,70,72,74,76,78,80,84,86,88,90,92,94,96,100,102,104,106,108,110,112,116,118,120,122,124,126,128,132,134,136,138,140,142,144,148,150,152,154,156,158,160,164,166,168,170,172,174,176,180,182,184,186,188,190,192,196,198,200,202,204,206,208,212,214,216,218,220,222,224,228,230,232,234,236,238,240,244,246,248,250,252,254,256,260,262,264,266,268,270,272,276,278,280,282,284,286,288,292,294,296,298,300,302,304,308,310,312,314,316,318,320,324,326,328,330,332,334,336,340,342,344,346,348,350,352,356,358,360,362,364,366,368,372,374,376,378,380,382,384,388,390,392,394,396,398,400,404,406,408,410,412,414,416,420,422,424,426,428,430,432,436,438,440,442,444,446,448,452,454,456,458,460,462,464,468,470,472,474,476,478,480,484,486,488,490,492,494,496,500,502,504,506,508,510,512,516,518,520,522,524,526,528,532,534,536,538,540,542,544,548,550,552,554,556,558,560,564,566,568,570,572,574,576,580,582,584,586,588,590,592,596,598,600,602,604,606,608,612,614,616,618,620,622 ,624,628,630,632,634,636,638,640,644,646,648,650,652,654,656,660,662,664,666,668,670,672,676,678,680,682,684,686,688,692,694,696,698,700,702,704,708,710,712,714,716,718,720,724,726,728,730,732,734,736,740,742,744,746,748,750,752,756,758,760,762,764,766,768,772,774,776,778,780,782,784,788,790,792,794,796,798,800,804,806,808,810,812,814,816,820,822,824,826,828,830,832,836,838,840,842,844,846,848,852,854,856,858,860,862,864,868,870,872,874,876,878,880,884,886,888,890,892,894,896,900,902,904,906,908,910,912,916,918,920,922,924,926,928,932,934,936,938,940,942,944,948,950,952,954,956,958,960,964,966,968,970,972,974,976,980,982,984,986,988,990,992,996,998,1000,1002,1004,1006,1008,1012,1014,1016,1018,1020,1022,1024
M＝600,N＝1024
511,767,765,763,759,751,831,735,863,879,887,509,507,891,893,895,503,703,495,927,938,941,939,943,479,639,882,885,889,923,925,883,935,946,947,949,877,919,951,953,875,447,859,861,871,911,955,957,855,959,761,967,754,757,383,747,749,755,827,829,823,847,970,743,971,733,973,975,978,731,979,727,701,815,719,981,699,983,505,985,987,799,498,501,695,989,255,475,477,487,491,493,499,635,637,687,471,991,994,671,631,995,997,999,1001,1003,1005,445,1007,463,1009,1010,443,623,1011,1013,1015,1017,993,439,1019,1021,1023,977,969,945,965,937,963,881,962,933,921,931,873,917,930,869,753,915,857,909,867,914,745,853,907,866,961,825,906,851,741,903,845,729,850,497,821,739,929,843,725,738,819,381,842,489,813,839,697,723,818,913,379,717,431,811,485,865,722,693,473,607,797,715,810,375,905,483,807,691,253,415,633,714,795,469,685,849,482,711,901,690,367,251,441,575,467,629,683,791,737,899,461,841,669,466,682,247,437,627,817,898,351,679,459,621,783,837,667,626,721,435,377,458,239,429,619,809,455,835,434,663,605,319,713,373,427,834,481,615,805,689,223,413,603,793,426,655,371,709,423,803,365,249,411,573,370,465,599,681,789,707,802,897,363,191,571,245,407,625,706,787,349,677,457,591,781,359,665,243,786,433,567,347,675,237,399,617,779,453,833,242,661,674,127,317,235,778,343,425,559,451,613,775,659,221,601,315,653,369,450,231,421,611,801,658,335,219,409,543,597,651,311,610,705,419,361,189,569,650,215,405,595,785,418,647,589,303,357,187,594,241,403,565,345,673,207,397,587,777,355,402,183,563,125,287,586,233,341,395,557,354,449,583,773,562,657,123,313,394,175,339,555,229,391,609,771,333,217,541,338,554,119,649,309,227,770,417,551,331,159,539,213,593,226,307,645,330,111,301,327,185,211,306,401,535,643,205,585,299,353,210,181,561,642,95,285,203,298,393,527,581,295,179,121,202,283,173,337,553,199,389,579,769,178,63,117,171,279,578,225,387,549,329,157,537,170,115,305,386,167,547,109,271,325,155,114,209,533,546,641,107,297,323,151,531,93,201,525,322,103,293,530,177,91,281,143,523,197,577,291,61,522,87,169,277,195,290,385,519,59,113 ,194,275,165,545,79,269,153,274,55,163,105,267,321,149,529,162,266,47,101,263,147,89,141,521,99,289,146,31,85,139,98,193,517,57,138,83,273,135,515,77,82,53,514,161,75,265,51,74,45,71,261,50,145,43,97,259,29,42,137,258,39,27,81,133,513,23,131,73,49,130,15,69,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,10,7,33,17,9,5,3,2,1,4,6,8,12,14,16,20,22,24,26,28,30,32,36,38,40,44,46,48,52,54,56,58,60,62,64,68,70,72,76,78,80,84,86,88,90,92,94,96,100,102,104,106,108,110,112,116,118,120,122,124,126,128,132,134,136,140,142,144,148,150,152,154,156,158,160,164,166,168,172,174,176,180,182,184,186,188,190,192,196,198,200,204,206,208,212,214,216,218,220,222,224,228,230,232,234,236,238,240,244,246,248,250,252,254,256,260,262,264,268,270,272,276,278,280,282,284,286,288,292,294,296,300,302,304,308,310,312,314,316,318,320,324,326,328,332,334,336,340,342,344,346,348,350,352,356,358,360,362,364,366,368,372,374,376,378,380,382,384,388,390,392,396,398,400,404,406,408,410,412,414,416,420,422,424,428,430,432,436,438,440,442,444,446,448,452,454,456,460,462,464,468,470,472,474,476,478,480,484,486,488,490,492,494,496,500,502,504,506,508,510,512,516,518,520,524,526,528,532,534,536,538,540,542,544,548,550,552,556,558,560,564,566,568,570,572,574,576,580,582,584,588,590,592,596,598,600,602,604,606,608,612,614,616,618,620,622,624,628,630,632,634,636,638,640,644,646,648,652,654,656,660,662,664,666,668,670,672,676,678,680,684,686,688,692,694,696,698,700,702,704,708,710,712,716,718,720,724,726,728,730,732,734,736,740,742,744,746,748,750,752,756,758,760,762,764,766,768,772,774,776,780,782,784,788,790,792,794,796,798,800,804,806,808,812,814,816,820,822,824,826,828,830,832,836,838,840,844,846,848,852,854,856,858,860,862,864,868,870,872,874,876,878,880,884,886,888,890,892,894,896,900,902,904,908,910,912,916,918,920,922,924,926,928,932,934,936,940,942,944,948,950,952,954,956,958,960,964,966,968,972,974,976,980,982,984,986,988,990,992,996,998,1000,1002,1004,1006,1008,1012,1014,1016,1018,1020,1022,1024
M＝720,N＝1024
767,895,950,951,954,955,957,511,959,943,974,975,982,983,986,987,893,989,890,891,991,998,999,886,887,927,1002,1003,1005,1007,879,1010,1011,1013,1014,1015,1017,1018,1019,1021,1023,863,765,762,763,759,758,751,831,1009,1001,997,735,995,985,994,981,979,509,978,973,506,507,953,971,970,503,502,949,947,967,946,966,703,941,938,495,939,935,934,889,925,885,922,923,883,882,877,479,919,918,874,875,871,870,639,910,861,911,858,859,761,855,854,757,447,755,754,749,846,829,746,847,747,826,827,743,742,823,822,733,730,731,727,726,815,383,505,701,718,501,719,698,699,499,993,498,493,977,799,695,694,490,491,969,945,965,487,486,477,687,963,937,474,475,962,637,255,933,634,635,471,931,470,921,930,881,917,631,630,445,671,462,873,915,463,442,443,914,869,909,867,62 3,857,439,438,907,866,906,853,851,903,850,902,431,753,845,825,745,381,607,843,842,821,378,379,741,819,739,729,839,375,818,374,813,838,738,415,725,810,811,723,722,717,367,807,697,575,806,715,797,714,693,794,795,253,497,691,711,690,250,251,685,489,710,351,791,790,682,683,246,247,485,483,473,482,633,679,678,782,669,469,239,783,629,467,666,667,627,466,319,626,461,621,441,459,663,662,618,458,619,437,223,435,455,434,615,429,454,614,654,605,655,426,427,602,603,377,423,422,961,599,598,413,373,191,410,411,929,371,370,573,365,590,591,407,406,570,571,362,363,913,567,865,566,359,358,905,398,349,399,849,346,347,901,899,249,127,841,898,737,817,837,721,809,835,713,834,481,805,689,793,709,803,465,681,789,707,802,897,245,625,706,787,677,457,781,665,243,786,433,675,237,617,779,453,833,242,661,674,317,235,778,343,425,559,451,613,775,659,221,601,234,315,342,653,369,450,231,774,421,611,801,658,335,219,314,409,543,597,651,230,311,610,705,419,334,361,218,189,569,650,215,310,405,595,785,418,647,589,303,357,187,214,594,241,403,565,646,345,673,207,397,587,777,186,355,402,183,563,125,206,287,586,233,341,395,557,354,449,583,773,182,562,657,123,313,394,175,339,555,582,229,391,609,771,333,122,217,541,338,554,119,649,309,390,227,770,417,551,331,159,539,118,213,593,226,307,550,645,330,111,301,538,327,185,211,306,401,535,643,205,585,299,326,353,210,534,181,561,642,95,285,203,298,393,527,581,295,179,121,202,283,526,173,337,553,199,294,389,579,769,178,282,63,117,171,198,279,578,225,387,549,329,157,537,170,278,115,305,386,167,547,109,271,325,155,114,209,533,166,546,641,270,107,297,154,323,151,531,93,106,201,525,322,103,293,150,530,177,91,281,143,523,102,197,577,291,90,61,142,522,87,169,277,195,290,385,519,59,86,113,194,275,518,165,545,79,269,58,153,274,55,163,78,105,267,321,54,149,529,162,266,47,101,263,147,89,141,521,262,99,289,146,31,85,139,98,193,517,57,138,83,273,135,515,77,82,53,134,514,161,75,265,51,74,45,71,261,50,145,43,70,97,259,29,42,137,258,39,27,81,38,133,513,26,23,131,73,22,49,130,15,69,14,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,10,7,6,33,17,9,5,3,2,1,4,8,12,16,20,24,28,30,32,36,40,44,46,48,52,56,60,62,64,68,72,76,80,84,88,92,94,96,100,104,108,110,112,116,120,124,126,128,132,136,140,144,148,152,156,158,160,164,168,172,174,176,180,184,188,190,192,196,200,204,208,212,216,220,222,224,228,232,236,238,240,244,248,252,254,256,260,264,268,272,276,280,284,286,288,292,296,300,302,304,308,312,316,318,320,324,328,332,336,340,344,348,350,352,356,360,364,366,368,372,376,380,382,384,388,392,396,400,404,408,412,414,416,420,424,428,430,432,436,440,444,446,448,452,456,460,464,468,472,476,478,480,484,488,492,494,496,500,504,508,510,512,516,520,524,528,532,536,540,542,544,548,552,556,558,560,564,568,572,574,576,580,584,588,592,596,600,604,606,608,612,616,620,622,624,628,632,636,638,640,644,648,652,656,660,664,668,670,672,676,680,684,686,688,692,696,700,702,704,708,712,716,720,724,728,732,734,736,740,744,748 ,750,752,756,760,764,766,768,772,776,780,784,788,792,796,798,800,804,808,812,814,816,820,824,828,830,832,836,840,844,848,852,856,860,862,864,868,872,876,878,880,884,888,892,894,896,900,904,908,912,916,920,924,926,928,932,936,940,942,944,948,952,956,958,960,964,968,972,976,980,984,988,990,992,996,1000,1004,1006,1008,1012,1016,1020,1022,1024
M＝768,N＝1024
894,895,958,767,959,766,990,991,999,989,987,998,1002,1003,986,1005,1006,983,1007,982,1010,1011,1013,1014,1015,975,957,1017,955,1018,974,1019,954,1021,951,1022,1023,511,950,510,943,942,893,891,890,927,887,926,886,879,878,863,765,763,862,762,759,758,1009,751,1001,750,997,831,995,985,830,994,981,979,735,978,973,971,734,953,509,970,949,507,947,967,506,946,503,966,941,939,502,938,935,703,889,495,702,925,934,923,494,885,883,922,882,919,877,875,918,874,479,871,478,911,861,870,859,639,910,858,761,638,855,757,755,854,754,447,749,747,829,847,827,446,746,846,826,743,823,733,742,731,822,730,993,727,815,505,726,977,814,383,501,499,969,701,382,699,719,498,945,493,718,698,965,491,963,695,799,937,490,694,798,962,487,933,931,477,486,921,475,687,881,930,474,686,917,637,915,873,471,255,635,634,254,470,869,914,867,909,631,907,671,857,445,630,443,463,866,670,853,906,442,462,851,623,903,439,753,850,438,622,845,902,843,825,745,431,821,741,842,819,739,839,430,729,607,381,379,818,738,606,813,838,725,378,811,723,375,810,722,415,374,717,807,697,715,414,497,797,367,806,693,575,795,714,691,366,711,489,574,794,690,685,791,710,485,253,683,483,251,473,790,250,351,682,482,247,633,679,469,350,467,246,629,783,669,678,627,667,466,782,461,239,441,459,626,666,621,961,663,619,238,437,458,319,435,929,662,618,318,455,615,434,429,454,427,223,605,655,614,913,603,222,426,865,654,377,602,905,423,599,373,413,422,371,411,598,849,901,899,370,410,365,191,573,841,407,363,571,190,591,406,362,570,590,898,359,567,817,837,737,835,349,399,358,566,347,809,249,398,346,721,245,559,343,834,127,243,805,803,558,713,126,342,242,793,237,689,235,709,802,317,707,789,315,335,787,234,681,231,706,314,334,543,677,786,481,311,221,465,897,625,457,781,665,433,675,617,779,453,833,661,674,778,425,451,613,775,659,601,653,369,450,774,421,611,801,658,219,409,597,651,230,610,705,419,361,218,542,189,569,650,215,310,405,595,785,418,647,589,303,357,187,214,594,241,403,565,646,345,673,207,302,397,587,777,186,355,402,183,563,125,206,287,586,233,341,395,557,354,449,583,773,182,562,657,286,123,313,394,175,339,555,582,229,391,609,771,333,122,217,541,174,338,554,119,649,309,390,227,770,417,551,331,159,539,118,213,593,226,307,550,645,330,111,301,158,538,327,185,211,306,401,535,643,110,205,585,299,326,353,210,534,181,561,642,95,285,203,298,393,527,581,295,179,94,121,202,283,526,173,337,553,199,294,389,579,769,178,282,63,117,171,198,279,578,2 25,387,549,329,62,157,537,170,278,115,305,386,167,547,109,271,325,155,114,209,533,166,546,641,270,107,297,154,323,151,531,93,106,201,525,322,103,293,150,530,177,91,281,143,523,102,197,577,291,90,61,142,522,87,169,277,195,290,385,519,59,86,113,194,275,518,165,545,79,269,58,153,274,55,163,78,105,267,321,54,149,529,162,266,47,101,263,147,89,46,141,521,262,99,289,146,31,85,139,98,193,517,30,57,138,83,273,135,515,77,82,53,134,514,161,75,265,51,74,45,71,261,50,145,43,70,97,259,29,42,137,258,39,27,81,38,133,513,26,23,131,73,22,49,130,15,69,14,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,10,7,6,33,17,9,5,3,2,1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,156,160,164,168,172,176,180,184,188,192,196,200,204,208,212,216,220,224,228,232,236,240,244,248,252,256,260,264,268,272,276,280,284,288,292,296,300,304,308,312,316,320,324,328,332,336,340,344,348,352,356,360,364,368,372,376,380,384,388,392,396,400,404,408,412,416,420,424,428,432,436,440,444,448,452,456,460,464,468,472,476,480,484,488,492,496,500,504,508,512,516,520,524,528,532,536,540,544,548,552,556,560,564,568,572,576,580,584,588,592,596,600,604,608,612,616,620,624,628,632,636,640,644,648,652,656,660,664,668,672,676,680,684,688,692,696,700,704,708,712,716,720,724,728,732,736,740,744,748,752,756,760,764,768,772,776,780,784,788,792,796,800,804,808,812,816,820,824,828,832,836,840,844,848,852,856,860,864,868,872,876,880,884,888,892,896,900,904,908,912,916,920,924,928,932,936,940,944,948,952,956,960,964,968,972,976,980,984,988,992,996,1000,1004,1008,1012,1016,1020,1024
M＝960,N＝1024
1022,1020,1023,1016,1021,1019,1018,1015,1014,1007,1012,1006,1004,991,990,1000,988,959,984,958,956,1017,1013,952,1011,895,1005,1010,894,1003,1002,892,999,989,998,987,888,986,767,996,983,766,982,957,975,955,764,980,974,954,951,972,950,760,511,943,893,948,510,942,891,1009,968,1001,890,508,940,887,927,997,886,926,985,879,995,936,504,765,981,884,878,924,994,763,979,973,876,953,762,863,978,920,759,971,949,862,758,970,872,751,947,941,967,860,509,756,750,946,831,966,939,889,507,830,856,938,748,735,885,506,925,964,935,503,734,828,883,923,877,934,744,502,882,495,922,732,875,919,932,824,703,500,494,761,993,874,861,918,871,702,911,728,757,977,859,492,479,870,916,910,755,700,969,858,749,478,639,855,868,754,945,829,488,747,908,965,854,638,696,476,847,827,746,447,937,733,505,963,743,846,852,826,904,636,446,731,933,501,823,742,472,962,921,881,844,730,822,499,931,815,444,727,740,493,632,701,873,917,383,498,814,820,930,726,491,719,840,699,869,915,382,440,909,490,718,799,724,812,698,857,477,914,487,867,695,907,380,798,753,475,853,716,486,637,694,866,687,255,808,906,474,745,851,796,635,903,845,471,686,692,484,825,376,254,44 5,712,741,850,634,902,470,843,463,821,671,631,443,684,729,792,739,252,842,630,462,468,442,819,670,623,900,725,813,839,439,738,961,680,497,818,622,628,723,460,381,668,438,811,838,248,431,717,697,489,929,722,607,810,379,620,797,430,436,715,693,836,807,456,664,485,378,606,714,795,913,691,375,415,806,473,428,616,685,711,483,794,374,604,865,690,414,367,575,253,633,469,905,683,710,791,804,482,424,366,372,574,251,629,467,682,790,849,412,783,669,461,600,901,441,708,679,250,466,627,351,364,667,621,572,782,459,841,788,247,678,437,899,408,626,350,666,619,458,246,737,817,435,239,837,663,429,676,360,780,455,568,898,618,348,434,605,238,319,662,244,809,377,721,615,427,655,454,835,603,318,373,614,426,776,713,223,654,660,805,236,413,344,452,834,423,602,793,371,689,222,599,411,365,612,316,803,422,573,709,652,370,232,598,789,410,481,591,681,363,571,802,220,707,191,407,420,249,312,362,590,596,787,570,648,349,677,406,465,781,359,399,190,706,245,567,216,665,625,347,786,358,588,675,398,566,457,404,243,779,559,237,188,346,617,661,127,242,343,433,674,356,558,453,564,317,778,235,396,584,613,659,126,342,775,425,184,335,653,315,234,543,451,221,601,556,231,658,611,774,334,340,897,314,392,421,124,219,542,651,311,230,450,597,610,409,369,552,218,650,332,419,310,772,303,595,215,540,228,120,647,589,189,361,405,569,833,418,302,308,214,594,207,646,328,187,587,357,403,565,536,397,206,287,212,300,186,345,801,586,402,355,563,183,644,395,286,557,583,241,341,204,182,125,354,705,562,175,296,785,394,555,582,233,339,284,123,391,333,174,313,180,200,554,122,338,541,229,673,580,777,390,551,331,119,159,309,172,280,217,539,227,550,657,330,118,773,307,158,111,388,213,301,327,168,538,226,116,110,306,535,548,156,609,449,211,299,326,649,205,771,185,534,210,95,298,527,108,593,417,285,152,181,203,94,295,324,645,532,770,526,202,283,294,179,104,585,173,199,401,643,92,282,178,63,561,524,121,171,198,353,279,62,292,581,393,88,170,278,642,117,157,271,196,167,553,579,337,389,520,115,60,155,276,270,109,166,549,329,578,114,387,154,537,107,225,305,547,151,164,268,325,56,386,106,533,93,297,150,546,209,103,143,323,531,91,769,641,201,525,322,293,530,177,281,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,59,86,140,113,194,275,518,165,545,79,269,58,153,84,274,55,136,516,163,78,105,267,321,54,149,529,162,76,266,47,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1,16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,304,320,336,352,368,384,400,416,432,448,464,480,496,512,528,544,560,576,592,608,624,640,656,672,688,704,720,736,752,768,784,800,816,832,848,864,880,896,912,928,944,960,976,992,1008,1024
M＝1200,N＝2048
1023,1021,1019,1015,1007,1471,1407,1503,991,1519,1527,1531,1533,1535,959,1529,1522,1525,1279,1517,1523,1515,1663,895,1499,1501,1511,1659,1661,1495,1695,1711,1655,1719,1723,1725,1467,1469,1487,1647,1463,1727,1743,1751,1755,1757,1759,1017,1767,1010,1011,1013,1455,767,1631,1005,1771,1405,1773,1775,1778,1003,1779,1403,1781,1783,1785,1787,1789,987,989,999,1391,983,1399,1439,1599,1791,1823,955,957,975,1375,1839,951,1777,1277,1847,1849,1851,1769,1275,1853,1842,1845,1855,511,1762,893,943,1263,1271,1738,1746,1747,1749,1753,1763,891,1343,1765,1834,1835,1837,1741,1843,1863,1831,1866,1867,1721,927,1869,887,1821,1739,1871,1874,1714,1875,1717,1877,1819,1879,1881,1883,1706,1885,1715,1247,1887,1735,1890,1891,879,1893,1709,1895,1815,1897,1521,1899,1901,1903,1707,1905,1906,1907,1513,1909,1911,1913,1915,1917,1919,1506,1509,1927,1703,1657,1930,1931,1497,1693,1933,1507,1807,863,1935,1650,1653,1938,1939,1490,1493,1691,765,1941,1943,1945,1651,1215,763,1482,1491,1947,1949,2047,2045,2043,2039,2031,2015,2041,1983,2037,2035,2029,2034,2027,2013,2023,2011,1981,2007,1979,2033,1999,1975,2025,1967,2021,2009,2019,1951,2005,2018,1977,2003,1997,2002,1973,1995,1971,1994,1965,1991,1970,1963,2017,1962,1959,2001,1993,1969,1989,1961,1987,1986,1957,1955,1954,1985,1953,1937,1889,1929,1009,1873,1925,1465,1001,1761,1923,1485,1865,1461,1841,1922,997,1483,1645,1861,985,1745,1459,1401,995,1453,1643,1833,1479,1859,1458,1687,981,1629,994,1737,1397,1451,1858,1505,1639,1829,953,1713,979,1437,1627,1817,1450,1679,1395,973,1733,1447,1827,1389,978,759,949,1273,1435,1597,1394,1489,1623,1705,1813,971,1731,1826,1921,1387,947,509,1595,889,1269,970,1431,1649,751,1730,1811,941,1373,1701,967,1481,1615,1805,946,1383,1689,507,831,1267,1810,1457,1591,885,939,1371,1699,993,1261,1423,1641,1803,1477,1857,735,1266,925,1685,938,503,1698,883,1151,1341,935,1259,1802,1367,1449,1583,877,1475,1637,1799,761,923,1683,882,977,1245,1625,1339,1677,1393,495,1474,875,1255,1445,1635,1825,703,1682,1359,757,919,1243,1433,1567,861,1621,1675,1335,969,1634,1729,1443,871,1385,755,945,1213,479,1593,1674,859,1239,1429,1619,749,1809,911,1442,1671,965,1613,754,1327,1381,1211,505,639,1618,829,1265,1427,1589,747,855,937,1369,1697,963,1231,1421,1611,1801,1379,733,447,1426,827,1207,501,1587,881,1149,962,1311,743,1610,933,1257,1365,1419,1581,847,1378,1473,1607,1797,731,921,1586,1681,499,823,1147,1337,1418,931,1199,1363,493,1579,873,1253,1415,1633,1795,701,1357,498,727,917,1241,1565,930,383,1362,1578,1143,1673,1333,491,815,1251,1794,1441,1575,869,699,1355,753,915,1183,477,1563,857,1237,1617,719,1250,1331,909,1669,487,1354,867,1135,1325,914,695,1351,1209,475,637,799,1235,1330,1425,1559,745,853,907,1667,866,961,1229,1609,1323,1377,255,1234,445,635,825,1205,906,471,1585,687,1666,851,1119,1309,741,903,1227,1322,1417,1551,8 45,1605,1319,729,443,1203,850,497,631,821,1145,1226,1307,739,929,1197,1361,463,1577,843,1223,1413,1603,1793,671,1202,725,439,738,819,1087,381,1141,1195,842,1303,489,623,1602,813,1249,1411,1573,839,697,1353,723,818,913,1181,1561,1194,379,1139,717,1329,431,1410,811,1191,485,1571,865,1133,722,1295,693,1349,1179,473,607,1138,797,1233,1557,715,810,375,905,1570,1665,483,807,1131,1321,691,1347,253,415,633,714,795,1175,469,1555,685,849,1117,482,711,901,1225,1549,690,367,1346,1127,1317,251,441,575,1554,1201,467,629,683,791,1115,1305,737,899,1167,461,1547,841,1221,1601,1315,669,466,682,247,437,627,817,1085,898,351,679,1546,1111,1193,1301,459,621,783,1219,1314,1409,1543,837,667,626,721,435,1083,377,458,1137,239,1218,1299,429,619,809,1189,455,1569,835,1103,1293,434,663,1177,605,319,1298,1079,713,373,427,1187,834,481,615,805,1129,1291,689,1345,223,413,603,793,1173,426,1553,655,1186,371,709,423,1290,803,1071,365,1125,1287,249,411,573,1171,370,465,599,681,789,1113,707,802,897,1165,1545,363,1123,1313,191,1170,571,245,407,625,706,787,1055,349,677,1109,1163,457,591,1122,781,1217,1541,359,665,243,786,433,567,1081,1162,347,675,1107,237,1297,399,617,779,1159,453,1539,833,1101,242,661,674,127,1106,317,1077,235,778,343,425,559,1538,1185,451,613,775,1099,1289,659,221,601,315,1075,653,369,450,231,1098,421,611,801,1069,658,335,1095,1285,219,409,543,1074,1169,597,651,311,610,705,419,1067,361,1121,1283,189,569,650,215,405,595,785,1053,418,647,1066,1161,589,303,1282,1063,357,187,594,241,403,565,1051,345,673,1105,207,397,587,777,1157,1537,355,402,183,563,125,287,586,1047,233,341,395,557,1155,354,449,583,773,1097,562,657,123,313,394,1073,175,1154,339,555,229,391,609,771,1039,333,1093,217,541,338,554,119,649,309,227,770,417,551,1065,331,1091,1281,159,539,213,593,226,307,645,330,111,1090,301,1061,327,185,211,306,401,535,1049,643,205,585,299,1059,353,210,181,561,642,95,285,1045,203,298,393,527,1058,1153,581,295,179,121,202,283,1043,173,337,553,199,389,579,769,1037,178,63,1042,117,171,279,578,225,387,549,1035,329,1089,157,537,170,115,305,386,167,1034,547,109,271,1031,325,155,114,209,533,546,641,107,297,1057,323,151,531,93,201,525,322,103,293,530,177,91,281,1041,143,523,197,577,291,61,522,87,169,277,195,290,385,519,1033,59,113,194,275,165,545,79,269,1029,153,274,55,163,105,267,1027,321,149,529,162,266,47,1026,101,263,147,89,141,521,99,289,146,31,85,139,98,193,517,57,138,83,273,135,515,77,82,53,514,161,75,265,1025,51,74,45,71,261,50,145,43,97,259,29,42,137,258,39,27,81,133,513,23,131,73,49,130,15,69,41,67,257,66,37,25,35,21,34,129,19,13,18,11,65,10,7,33,17,9,5,3,2,1,4,6,8,12,14,16,20,22,24,26,28,30,32,36,38,40,44,46,48,52,54,56,58,60,62,64,68,70,72,76,78,80,84,86,88,90,92,94,96,100,102,104,106,108,110,112,116,118,120,122,124,126,128,132,134,136,140,142,144,148,150,152,154,156,158,160,164,166,168,172,174,176,180,182,184,186,188,190,192,196,198,200,204,206,208,212,214,216,218,220,222,224,228,230,232,234,236,238 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4,1806,1808,1812,1814,1816,1818,1820,1822,1824,1828,1830,1832,1836,1838,1840,1844,1846,1848,1850,1852,1854,1856,1860,1862,1864,1868,1870,1872,1876,1878,1880,1882,1884,1886,1888,1892,1894,1896,1898,1900,1902,1904,1908,1910,1912,1914,1916,1918,1920,1924,1926,1928,1932,1934,1936,1940,1942,1944,1946,1948,1950,1952,1956,1958,1960,1964,1966,1968,1972,1974,1976,1978,1980,1982,1984,1988,1990,1992,1996,1998,2000,2004,2006,2008,2010,2012,2014,2016,2020,2022,2024,2026,2028,2030,2032,2036,2038,2040,2042,2044,2046,2048
M＝1440,N＝2048
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M＝2400,N＝4096
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Claims (24)

  1. 一种编码方法，其特征在于，包括：
    确定N个待编码比特，N为正整数；
    获取包含N个极化信道序号的第一序列；
    根据所述第一序列确定所述N个待编码比特中信息比特的位置；
    对所述N个待编码比特进行Polar编码以得到编码比特。
  2. 如权利要求1所述的方法，其特征在于，所述确定N个待编码比特包括：
    根据M确定N,其中，N＝M，所述M为Polar码输出的目标码长，所述M等于2的正整数次幂，M为正整数。
  3. 如权利要求2所述的方法，其特征在于，所述获取包含N个极化信道序号的第一序列包括：
    从附录表1中序列或表1中序列的等同替换序列得到包含N个极化信道序列的第一序列。
  4. 如权利要求1所述的方法，其特征在于，所述确定N个待编码比特包括：
    根据M确定N,其中，
    Figure PCTCN2018073435-appb-100001
    符号
    Figure PCTCN2018073435-appb-100002
    表示向下取整，所述M为Polar码输出的目标码长，所述M不等于2的正整数次幂，M为正整数。
  5. 如权利要求4所述的方法，其特征在于，所述N个待编码比特对应码长为N的母码，
    所述获取包含N个极化信道序号的第一序列包括：
    根据通信系统支持的最大母码码长N max对应的最大第一序列S max确定所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
  6. 如权利要求5所述的方法，其特征在于，所述最大第一序列S max为附录表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
    所述获取包含N个极化信道序号的第一序列包括：
    确定所述N个编码比特中要删除的N-M个比特的位置；
    依次读取所述最大第一序列S max中极化信道序号，并且将所述最大第一序列S max中不在所述N-M个比特的位置且不大于N的极化信道序号依次读出；
    当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成 的序列为所述母码码长N所对应的所述第一序列。
  7. 如权利要求4所述的方法，其特征在于，所述N个待编码比特对应码长为N的母码，
    所述获取包含N个极化信道序号的第一序列包括：
    根据在无需进行速率匹配时所述母码码长N所对应的第四序列，确定在需要进行速率匹配时所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
  8. 如权利要求7所述的方法，其特征在于，所述第四序列为附录中表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
    所述根据母码码长N在无需进行速率匹配时所对应的第四序列，确定所述母码码长N所对应的第一序列包括：
    确定所述N个编码比特中要删除的N-M个比特的位置；
    依次读取第四序列中极化信道序号，并且将第四序列中不在所述N-M个比特的位置的极化信道序号依次读出；
    当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为所述母码码长N在需要进行速率匹配时所对应的第一序列。
  9. 如权利要求4所述的方法，其特征在于，所述获取包含N个极化信道序号的第一序列包括：
    从附录中表2、表3或表4中序列或者所述表2、表3或表4中序列的等同替换序列得到包含N个极化信道序列的第一序列。
  10. 如权利要求1、2或4所述的方法，其特征在于，所述获取包含N个极化信道序号的第一序列包括：
    根据N个第二序列S 1，S 2，…,S N确定第一序列S′ N，第二序列S i包含i个极化信道序号，1≤i≤N，i为正整数。
  11. 如权利要求10所述的方法，其特征在于，所述根据N个第二序列S 1，S 2，…,S N确定第一序列S′ N包括：
    确定N个第二序列S 1，S 2，…,S N；
    初始化第一序列S′ 1＝S 1；
    设置j从2遍历到N，基于如下公式计算得到第一序列S′ N：
    S′ j＝S′ j-1+(S′ j-1\S j)
    其中，2≤j≤N，j为正整数，“\”表示计算两个序列的差集，“+”表示将前后两个序列进行连接以形成一个序列。
  12. 一种编码装置，其特征在于，包括：
    确定模块，用于确定N个待编码比特，N为正整数；
    获取模块，用于获取包含N个极化信道序号的第一序列；
    所述确定模块，还用于根据所述第一序列确定所述N个待编码比特中信息比特的位置；
    所述编码模块，用于对所述N个待编码比特进行Polar编码以得到编码比特。
  13. 如权利要求12所述的装置，其特征在于，所述确定模块具体用于：
    根据M确定N,其中，N＝M，所述M为Polar码输出的目标码长，所述M等于2的正整数次幂，M为正整数。
  14. 如权利要求13所述的装置，其特征在于，所述获取模块具体用于：
    从附录表1中序列或表1中序列的等同替换序列得到包含N个极化信道序列的第一序列。
  15. 如权利要求12所述的装置，其特征在于，所述确定模块具体用于：
    根据M确定N,其中，
    Figure PCTCN2018073435-appb-100003
    符号
    Figure PCTCN2018073435-appb-100004
    表示向下取整，所述M为Polar码输出的目标码长，所述M不等于2的正整数次幂，M为正整数。
  16. 如权利要求15所述的装置，其特征在于，所述N个待编码比特对应码长为N的母码，
    所述获取模块具体用于：
    根据通信系统支持的最大母码码长N max对应的最大第一序列S max确定所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
  17. 如权利要求16所述的装置，其特征在于，所述最大第一序列S max为附录表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
    所述获取模块具体用于：
    确定所述N个编码比特中要删除的N-M个比特的位置；
    依次读取所述最大第一序列S max中极化信道序号，并且将所述最大第一序列S max中不在所述N-M个比特的位置且不大于N的极化信道序号依次读出；
    当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成 的序列为所述母码码长N所对应的所述第一序列。
  18. 如权利要求15所述的装置，其特征在于，所述N个待编码比特对应码长为N的母码，
    所述获取模块具体用于：
    根据在无需进行速率匹配时所述母码码长N所对应的第四序列，确定在需要进行速率匹配时所述母码码长N所对应的第一序列，其中，所述母码码长N所对应的第一序列为所述包含N个极化信道序号的第一序列。
  19. 如权利要求18所述的装置，其特征在于，所述第四序列为附录中表1中序列或表1中序列的等同替换序列之一，所述N个待编码比特对应N个编码比特；
    所述获取模块具体用于：
    确定所述N个编码比特中要删除的N-M个比特的位置；
    依次读取第四序列中极化信道序号，并且将第四序列中不在所述N-M个比特的位置的极化信道序号依次读出；
    当读出的极化信道序号的数量达到N时，确定已经读出的N个极化信道序号所组成的序列为所述母码码长N在需要进行速率匹配时所对应的第一序列。
  20. 如权利要求15所述的装置，其特征在于，所述获取模块具体用于：
    从附录中表2、表3或表4中序列或者所述表2、表3或表4中序列的等同替换序列得到包含N个极化信道序列的第一序列。
  21. 如权利要求12、13或15所述的装置，其特征在于，所述获取模块具体用于：
    根据N个第二序列S 1，S 2，…,S N确定第一序列S′ N，第二序列S i包含i个极化信道序号，1≤i≤N，i为正整数。
  22. 如权利要求21所述的装置，其特征在于，所述获取模块具体用于：
    确定N个第二序列S 1，S 2，…,S N；
    初始化第一序列S′ 1＝S 1；
    设置j从2遍历到N，基于如下公式计算得到第一序列S′ N：
    S′ j＝S′ j-1+(S′ j-1\S j)
    其中，2≤j≤N，j为正整数，“\”表示计算两个序列的差集，“+”表示将前后两个序列进行连接以形成一个序列。
  23. 一种通信装置，其特征在于，包括：
    存储器，用于存储程序；
    处理器，用于执行所述存储器存储的所述程序，当所述程序被执行时，所述处理器用于执行如权利要求1-11中任一所述的步骤。
  24. 一种计算机可读存储介质，包括指令，当其在计算机上运行时，使得计算机执行如权利要求1-11任意一项所述的方法。
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