JP2004142195A - Method for controlling recording position - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To update the period of a timing signal with high response to speed variation of a carriage. <P>SOLUTION: When recording is performed by scanning a recording medium with a carriage mounting a recording head having a recording element and a timing signal defining the driving timing of the recoding element is generated, periods of the rising and falling edges of a pulse signal being delivered from an encoder depending on the position of the carriage in the scanning direction are measured. When the period of the timing signal is calculated by dividing the period of the edge by a specified number, division is performed after a remainder produced in the previous calculation is added to the period of the edge and then the period of the timing signal is updated based on the calculation results. <P>COPYRIGHT: (C)2004,JPO

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to control of a print position, and more particularly to generation of a timing signal for defining a drive timing of a print element when printing is performed by scanning a carriage mounted with a print head having a print element on a print medium. is there.
[0002]
[Prior art]
For example, as an information output device in a word processor, a personal computer, a facsimile, or the like, a recording device that records desired information such as characters and images on a sheet-like recording medium such as paper or a film is used to feed a recording medium such as paper. A serial recording method for performing recording by scanning a carriage equipped with a recording head having a recording element in a direction intersecting the direction is generally widely used from the viewpoint of low cost and easy downsizing.
[0003]
Various types of recording methods are known for the recording apparatus, but the ink jet method is used because non-contact recording is possible on a recording medium such as paper, colorization is easy, and quietness is high. In recent years, it has received special attention.
[0004]
In such a printing apparatus, it is essential to match the scanning position of the print head with the drive timing of the print head. As a means for detecting the scanning position of the recording head, an encoder or the like for detecting a moving position of a carriage on which the recording head is mounted is used.
[0005]
When an encoder is used, the resolution at which the position of the carriage is detected by the encoder has a significant effect on the image recording resolution. It is an important issue to improve the recording resolution (resolution) of an image. In order to increase the recording resolution of an image in a recording apparatus using such an encoder, it is general to increase the resolution of the encoder. It is. However, at present, there is a demand for a low-priced inkjet recording apparatus, and the use of a high-resolution, high-priced encoder is a negative factor in terms of cost in commercializing the recording apparatus.
[0006]
In such a situation, in order to suppress the increase in the cost of the entire apparatus while achieving a higher resolution of the recorded image, a timing signal (kick pulse) having a higher resolution is required based on the pulse-like encode signal output from the encoder. ) And drive the recording head based on this signal.
[0007]
As a method of generating a high-resolution signal, there is a method of equally dividing one cycle from a rising edge of a encode signal output from an encoder to a next rising edge (or a falling edge to a next falling edge) by n. Used. For example, assuming that the immediately preceding edge cycle measurement value is m and the number of kick pulses (the number of divisions) generated within a preset edge cycle is n, the kick pulse interval is a quotient of m / n, and n After the kick pulse is generated, the process waits until the next edge cycle.
[0008]
FIG. 2 is a block diagram showing a configuration of a conventional kick pulse control circuit. Reference numeral 1 denotes an edge detector, which generates a start pulse when detecting the edge interval of the encode signal. Reference numeral 2 denotes a counter for measuring an edge interval (period). Reference numeral 3 denotes a shifter, which performs an operation corresponding to division when n is a power of 2. Reference numeral 4 denotes a register for holding an edge interval. Reference numeral 5 denotes a selector for selecting a shifter value or a register value. Reference numeral 6 denotes a load counter for loading data in response to a load signal. Reference numeral 7 denotes a 1 detector which outputs "H" when the value of the load counter is 1. A pulse controller 8 controls the number of kick pulses.
[0009]
In this circuit, when an edge of the encode signal is detected, a start pulse is generated by the edge detector 1. A value obtained by subtracting the margin value from one cycle of the edge measured by the counter 2 by the start pulse and dividing by the number of kick pulses generated between the slits is stored in the register 4. The selector 5 outputs the output of the shifter 3 or the value of the register 4 according to a control signal generated from the pulse controller 8.
[0010]
The counter 6 performs data loading on the output of the selector by the load signal output from the pulse controller 8, and decrements each time a clock is input until the loaded data becomes 1. This time is the kick pulse interval. When the value of the counter 6 is 1, the one detector 7 outputs an ON portion for one clock of the kick pulse. When a pulse is generated, the pulse controller 8 outputs a load signal to the counter 6. The number of pulses output at that time is counted, and a load signal is output to the counter 6 until the count value reaches the number of kick pulses generated between the slits.
[0011]
FIG. 1 is a timing chart showing the relationship between the two-phase encode signals S1 and S2 output from the encoder and the kick pulse P1 generated by the kick pulse control circuit as shown in FIG. In this example, a kick pulse corresponding to a recording resolution of 1200 dpi corresponding to eight times is generated from an encoded signal of an encoder having a resolution of 150 dpi. It should be noted that the numbers in the figure indicate the count number of the clock.
[0012]
For example, when the interval of one cycle measured at the rising edge of the encoder signal S1 changes from 79 of the interval A from time t0 to t1 to 84 of the interval B from time t1 to t2, the kick pulse interval in the interval B (Cycle) is based on the immediately preceding interval A,
79/8 = 9 ... 7 remainder
From this calculation, the kick pulse interval is 9. In this case, after the eighth kick pulse is output, until the next kick pulse is output,
84-9 × 8 = 12 (clock)
Is too long.
[0013]
As described above, in the case where the recording operation is performed while the carriage is performing the deceleration operation, a portion having a gap is generated.
[0014]
On the other hand, when the interval of one cycle measured at the rising edge of the encoder signal S1 changes from 84 of the interval B from time t1 to t2 to 76 of the interval C from time t2 to t3, the kick pulse interval at the interval C Is based on the immediately preceding interval B,
84/8 = 10 ... Remainder 4
From this calculation, the kick pulse interval is 10. In this case, the eight kick pulses do not fit in the interval C. In the next interval D, the kick pulse is generated after the eighth kick pulse generated in the interval C is output, or before the kick pulse generated for the interval C is output, A kick pulse for the next interval D is output.
[0015]
As described above, when the recording operation is performed while the carriage is accelerating, the recording may not be performed at the target position.
[0016]
[Problems to be solved by the invention]
As shown in FIG. 1, two signals of the A phase (S1) and the B phase (S2) are output from the encoder, but the phase of the A phase signal is originally shifted by 90 ° for the B phase signal. Things. Therefore, if the edge interval and the rise-fall interval between the A and B phases are accurate, an accurate quadrupled signal can be generated based on these two signals.
[0017]
However, in actuality, due to the mounting accuracy of the encoder, the characteristics of the photodiode, the accuracy of the slit provided in the film, and the like, an error occurs in the duty ratio in the same phase and the interval accuracy between the A and B phases. It is difficult to perform high-resolution recording even using the quadrupled signal.
[0018]
For this reason, conventionally, a kick pulse interval is calculated by using a reliable A-phase or B-phase edge interval as shown in FIG. While measuring one cycle of the edge from the encode signal, it is conceivable that the speed of the carriage fluctuates in a short time shorter than one cycle of the edge due to mechanical factors. However, in the conventional method, since one cycle of the edge is measured based on only one encode signal, the time required for measuring the cycle becomes longer, and the response to a change in the speed of the carriage is delayed.
[0019]
As described above, according to the conventional method, the response of the kick pulse to the speed fluctuation of the carriage is delayed, and therefore, it is difficult to perform high-quality recording especially during the acceleration / deceleration operation of the carriage.
[0020]
The present invention has been made in view of the above situation, and an object of the present invention is to update the cycle of a timing signal with good responsiveness to a speed variation of a carriage.
[0021]
[Means for Solving the Problems]
A print position control method according to one embodiment of the present invention that achieves the above object specifies a drive timing of a print element when printing is performed by scanning a carriage equipped with a print head having a print element on a print medium. A recording position control method for generating a timing signal,
Measure the cycle of the rising and falling edges of the pulse signal output from the encoder according to the position of the carriage in the scanning direction,
The cycle of the timing signal is calculated by dividing the cycle of the edge by a predetermined number,
Updating the cycle of the timing signal based on the calculation result;
At the time of the calculation, the division is performed after the remainder generated in the previous calculation is added to the cycle of the edge.
[0022]
That is, according to the present invention, when generating a timing signal that specifies the drive timing of the recording element when performing recording by scanning a carriage equipped with a recording head having a recording element on a recording medium, the scanning direction of the carriage is The rising and falling edges of the pulse signal output from the encoder are measured in accordance with the position of the edge signal, and the cycle of the timing signal is calculated by dividing the cycle of the edge by a predetermined number. Is added to the cycle of the edge, division is performed, and the cycle of the timing signal is updated based on the calculation result.
[0023]
In this way, each time a rising edge or a falling edge of the pulse signal output from the encoder is detected, the remainder in the previous calculation is added to the period of the detected edge, and the result is divided by a predetermined number. Then, the cycle of the timing signal is calculated and updated.
[0024]
Therefore, even in an acceleration / deceleration region where the moving speed of the carriage is not constant or when there is a speed fluctuation, the cycle of the timing signal is updated to an appropriate value with good responsiveness.
[0025]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.
[0026]
In the embodiments described below, a printer using an inkjet recording method will be described as an example of a recording apparatus to which the present invention is applied.
[0027]
In the present specification, “recording” (sometimes referred to as “printing”) refers not only to forming significant information such as characters and figures, but also to meaningless or insignificant human perception. Regardless of whether or not the image is exposed, a case where an image, a pattern, a pattern, or the like is widely formed on a recording medium or a case where the medium is processed is also described.
[0028]
In addition, the term “recording medium” refers to not only paper used in general recording devices, but also a wide range of materials that can accept ink, such as cloth, plastic films, metal plates, glass, ceramics, wood, and leather. Shall be.
[0029]
Further, “ink” (sometimes referred to as “liquid”) is to be interpreted broadly as in the definition of “recording (printing)”, and when applied on a recording medium, an image or pattern , Or a liquid that can be used for forming a pattern or the like, processing a recording medium, or processing ink (for example, coagulation or insolubilization of a colorant in ink applied to a recording medium).
[0030]
In the following description, the expression “interval” of a signal or an edge means the same time interval (period) as the cycle of the signal or the edge.
[0031]
<Schematic description of the device body>
FIG. 7 is an external perspective view showing an outline of a configuration of an inkjet printer IJRA suitable for applying the present invention. In FIG. 7, the carriage HC that engages with the spiral groove 5004 of the lead screw 5005 that rotates via the driving force transmission gears 5009 to 5011 in conjunction with the forward and reverse rotation of the drive motor 5013 has a pin (not shown). Then, it is supported by the guide rail 5003 and reciprocates in the directions of arrows a and b. On the carriage HC, an integrated type ink jet cartridge IJC containing a recording head IJH and an ink tank IT is mounted.
[0032]
Reference numeral 5002 denotes a paper pressing plate, which presses the recording paper P against the platen 5000 in the moving direction of the carriage HC. Reference numerals 5007 and 5008 denote photocouplers, which are home position detectors for confirming the presence of the carriage lever 5006 in this area and switching the rotation direction of the motor 5013.
[0033]
Reference numeral 5016 denotes a member that supports a cap member 5022 that caps the front surface of the print head IJH. Reference numeral 5015 denotes a suction device that suctions the inside of the cap, and performs suction recovery of the print head through an opening 5023 in the cap. Reference numeral 5017 denotes a cleaning blade. Reference numeral 5019 denotes a member that allows the blade to move in the front-rear direction. These members are supported by a main body support plate 5018. It goes without saying that the blade is not limited to this form and a known cleaning blade can be applied to the present embodiment.
[0034]
Reference numeral 5021 denotes a lever for starting suction for recovery from suction, which moves with the movement of the cam 5020 which engages with the carriage, and the driving force from the driving motor is controlled by a known transmission mechanism such as clutch switching. Is done.
[0035]
These capping, cleaning, and suction recovery are configured so that desired operations can be performed at the corresponding positions by the action of the lead screw 5005 when the carriage comes to the area on the home position side. If the above operation is performed, any of the embodiments can be applied.
[0036]
<Description of control configuration>
Next, a control configuration for executing the recording control of the above-described apparatus will be described.
[0037]
FIG. 8 is a block diagram showing a configuration of a control circuit of the inkjet printer IJRA. In the figure showing a control circuit, 1700 is an interface for inputting a print signal, 1701 is an MPU, 1702 is a ROM for storing a control program executed by the MPU 1701, and 1703 is various data (the print signal and print data supplied to the head). Etc.) are stored in the DRAM. A gate array (GA) 1704 controls supply of print data to the print head IJH, and also controls data transfer between the interface 1700, the MPU 1701, and the RAM 1703. Reference numeral 1710 denotes a carrier motor for transporting the recording head IJH, and reference numeral 1709 denotes a transport motor for transporting the recording paper. Reference numeral 1705 denotes a head driver for driving the recording head, and 1706 and 1707 denote motor drivers for driving the transport motor 1709 and the carrier motor 1710, respectively.
[0038]
The operation of the above control configuration will be described. When a print signal enters the interface 1700, the print signal is converted into print data between the gate array 1704 and the MPU 1701. Then, the motor drivers 1706 and 1707 are driven, and the recording head is driven in accordance with the recording data sent to the head driver 1705 to perform recording.
[0039]
In this example, the control program executed by the MPU 1701 is stored in the ROM 1702. However, an erasable / writable storage medium such as an EEPROM is further added, and the control program is changed from a host computer connected to the inkjet printer IJRA. It can be configured to be able to do so.
[0040]
As described above, the ink tank IT and the recording head IJH may be integrally formed to constitute a replaceable ink cartridge IJC. However, the ink tank IT and the recording head IJH may be configured to be separable. Then, when the ink runs out, only the ink tank IT may be replaced.
[0041]
<Kick pulse control circuit>
A kick pulse control circuit used in the ink jet printer having the above configuration will be described.
[0042]
FIG. 3 is a block diagram of a kick pulse control circuit for generating a heat pulse which is a drive signal of a recording head in the above-described inkjet printer. The kick pulse control circuit according to the present embodiment includes an edge interval capturing section 9 and a pulse interval calculating section 10.
[0043]
The kick pulse control circuit receives two signals of the A phase and the B phase from the encoder. The edge interval capturing unit 9 sets the rising edge interval of the A phase, the rising edge interval of the B phase, A value is output in the order of the falling edge interval of the A phase and the falling edge interval of the B phase. In the present embodiment, a free-run counter is used as a counter for measuring the edge interval. The pulse interval calculation unit 10 fetches these edge interval values, performs processing such as surplus propagation processing, updating the pulse interval during generation by updating the edge interval values, and outputs kick pulses.
[0044]
Hereinafter, the kick pulse control circuit according to the present embodiment will be described in detail with reference to FIGS. FIG. 4 is a block diagram showing a detailed configuration of the edge interval capturing section 9, and FIG. 5 is a block diagram showing a detailed configuration of the pulse interval calculating section 10. FIG. 6 is a timing chart showing the relationship between the A-phase and B-phase signals input to the kick pulse control circuit and the output kick pulse.
[0045]
In FIG. 4 showing the detailed configuration of the edge interval capturing section 9, reference numeral 15 denotes a free-run counter, which starts counting up a clock simultaneously with the start of kick pulse generation processing. Reference numerals 11 to 14 denote edge detectors, which generate a start pulse when an A-phase rising, an A-phase falling, a B-phase rising, and a B-phase falling are detected in order. Reference numerals 17 to 20 denote registers provided in correspondence with the edge detectors 11 to 14, respectively. When a start pulse is generated from the corresponding edge detector, the register holds the value of the free-run counter 15 at that time.
[0046]
Reference numeral 21 denotes a controller which outputs the value of a register connected to the edge detector which has generated the start pulse via a selector 22. For example, when an A-phase rising edge is detected, the controller 21 outputs the value of the register 17 via the selector 22 by a start pulse generated from the edge detector 11. A subtractor 23 subtracts the output value of the selector 22 from the output value of the free-run counter 15. Reference numeral 24 denotes a register which holds the value output from the subtractor 23. That is, each time an edge is measured, the value is stored in the register 24 in the order of the A-phase rising one cycle interval value, the B-phase rising one cycle interval value, the A-phase falling one cycle interval value, and the B-phase falling one cycle interval value. Will be retained.
[0047]
Reference numeral 16 denotes a comparator which compares the value of the register 17 with the value of the free-run counter 15 and sets an overflow bit as error processing when the values match (when the free-run counter exceeds the measurable range). Here, the value of the register 17 is compared with the value of the free-run counter 15, but the register to be compared may be any of the registers 17 to 20.
[0048]
In FIG. 5 showing the detailed configuration of the pulse interval calculation unit 10, a register 25 holds a remainder generated from the previous calculation m / n for calculating the kick pulse interval. The adder 26 adds the one-period interval value output from the edge interval capturing unit 9 to the value held in the register 25. Then, the kick pulse interval value is obtained from the edge one cycle interval value by the register 25, the adder 26, and the shifter 27. In the division of m / n, which is a calculation for calculating the kick pulse interval, the shifter 27 is used because the divisor is a power of two.
[0049]
The register 28 holds the remainder resulting from the calculation m / n for calculating the kick pulse interval two times before. The kick pulse that is being generated when the edge one cycle interval value is updated by the adder 29, the register 28, and the shifter 30 using the edge one cycle interval value and the remainder obtained in the calculation for calculating the kick pulse interval two times before. An interval change value is determined.
[0050]
The register 32 holds the kick pulse interval value to be generated. The counter 33 is set to 1 by the comparator 34 and counts up each time a clock is input. The comparator 34 compares the value of the register 32 with the value of the counter 33, and outputs a signal corresponding to the kick pulse ON when the counter value is 1 for one clock period. After that, a signal corresponding to the OFF of the kick pulse is output until the value of the register 32 matches the counter value, and the value of the counter 33 is set to 1.
[0051]
The comparator 35 compares the kick pulse interval value being generated held in the register 32 with the kick pulse change value when the edge 1 cycle interval value from the shifter 30 is updated, and the value of the counter 33 determines the change value. If not exceeded, the value of the register 32 is changed to the value of the shifter 30 at the time of updating the edge one cycle interval value. However, when the value of the counter 33 is larger than the value of the shifter 30, this processing is performed after the next kick pulse is generated.
[0052]
That is, only when the changed value is smaller than the current interval and the value of the counter 33 (the current count value) is larger than the changed value, the kick pulse interval is changed after the next kick pulse is generated.
[0053]
The kick pulse is ANDed with the overflow signal output from the edge interval capturing section 9, and is not output in the case of overflow.
[0054]
As described above, in the present embodiment, the rising and falling edge interval values of the A-phase and the B-phase output from the encoder are fetched, the remainder is propagated, and the updating of the pulse interval during generation by updating the edge interval value is performed. Performs processing and outputs a kick pulse.
[0055]
These processes will be described with reference to the timing chart of FIG. In FIG. 6, S3 and S4 are A-phase and B-phase signals output from the encoder, and P2 is a kick pulse output.
[0056]
If the falling period interval of the B phase measured from time t7 to t11 is 79 and the remainder is 2 by the kick pulse interval calculation immediately before t11, the leading pulse at t11 is:
(79 + 2) / 8 = 10 ... Remainder 1
And the first pulse interval at t11 is 10. Due to the propagation of the remainder, the next pulse interval is
(79 + 1) / 8 = 10: remainder 0
And the pulse interval is set to 10.
[0057]
While a pulse is being generated at this interval, the rising period interval of the A phase measured from t8 to t12 is measured, and this value is 76. Therefore, when the pulse interval is calculated again based on this value,
(76 + 1) / 8 = 9 remainder 5
It becomes. At this time, the pulse interval being generated is updated from 10 to 9 at the time of updating the edge interval at t12.
[0058]
Therefore, according to the embodiment described above, since the extra propagation processing is performed, a kick pulse with good responsiveness to a speed change can be generated even in an area where the carriage is accelerating or decelerating.
[0059]
In the above-described embodiment, the propagated remainder is reset at the start of the carriage scanning. When recording is performed by reciprocating scanning, the complement at the time of generation of the last pulse in the forward path is used as the remainder at the start position of the return path. When the pulse interval is equal to or smaller than the minimum pulse interval which is a threshold value for compensating all nozzle discharges, the pulse interval is set to the minimum pulse interval.
[0060]
<Other embodiments>
In the above-described embodiment, the present invention is applied to an ink-jet type recording apparatus. However, the present invention employs another method as long as the recording apparatus performs recording by scanning a carriage equipped with a recording head. It can also be applied to a recording device.
[0061]
Furthermore, the kick pulse interval may be obtained by dividing by a number other than the edge interval division number (8) in the above embodiment. Also, the kick pulse may be generated based on the interval between the rising and falling edges of either the A phase or the B phase, instead of both the A phase and the B phase of the encoder signal.
[0062]
The present invention can be realized as a recording position control method in a recording apparatus as described above. A recording apparatus that performs the recording position control method, a computer program that causes a computer to execute the recording position control method, and a computer program Can be realized in the form of a storage medium for storing the information. Specifically, even when applied to a system including a plurality of devices (for example, a host computer, an interface device, a reader, a printer, etc.), a single device (For example, a copying machine, a facsimile machine, etc.).
[0063]
Further, an object of the present invention is to provide a storage medium storing a program code of software for realizing the functions of the above-described embodiments to a system or an apparatus, and a computer (or CPU or MPU) of the system or apparatus to store the storage medium. It is needless to say that the present invention can also be achieved by reading and executing the program code stored in the program.
[0064]
In this case, the program code itself read from the storage medium realizes the function of the above-described embodiment, and the storage medium storing the program code constitutes the present invention.
[0065]
As a storage medium for supplying the program code, for example, a floppy disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a CD-R, a magnetic tape, a nonvolatile memory card, a ROM, and the like can be used.
[0066]
When the computer executes the readout program code, not only the functions of the above-described embodiments are realized, but also an OS (Operating System) running on the computer based on the instruction of the program code. It goes without saying that a part or all of the actual processing is performed and the functions of the above-described embodiments are realized by the processing.
[0067]
Further, after the program code read from the storage medium is written into a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer, the function expansion is performed based on the instruction of the program code. It goes without saying that a CPU or the like provided in the board or the function expansion unit performs part or all of the actual processing, and the processing realizes the functions of the above-described embodiments.
[0068]
【The invention's effect】
As described above, according to the present invention, each time the rising edge and the falling edge of the pulse signal output from the encoder are detected, the remainder in the previous calculation is added to the cycle of the detected edge. The period of the timing signal is calculated by dividing it by a predetermined number and updated.
[0069]
Therefore, even in an acceleration / deceleration region where the moving speed of the carriage is not constant or when there is a speed fluctuation, the cycle of the timing signal is updated to an appropriate value with good responsiveness.
[Brief description of the drawings]
FIG. 1 is a timing chart of a kick pulse generated by a conventional method.
FIG. 2 is a block diagram showing a configuration of a conventional kick pulse control circuit.
FIG. 3 is a block diagram showing a schematic configuration of a kick pulse control circuit according to the present invention.
FIG. 4 is a block diagram illustrating a configuration of an edge interval capturing unit in FIG. 3;
FIG. 5 is a block diagram illustrating a configuration of a pulse interval calculation unit in FIG. 3;
FIG. 6 is a timing chart of a kick pulse generated according to the present invention.
FIG. 7 is a view showing the appearance of the ink jet printer according to the present invention.
FIG. 8 is a block diagram illustrating a control configuration of the printer of FIG. 7;
[Explanation of symbols]
S1, S3 Encoded signal (A phase)
S2, S4 Encoded signal (B phase)
P1, P2 Kick pulse 1 Edge detector 2, 6 Counter 3 Shifter 4 Register 5 Selector 7 1 detector 8 Pulse controller 9 Edge interval capture unit 10 Pulse interval calculation unit 11, 12, 13, 14 Edge detector 15 Free-run counter 16, 34, 35 Comparators 17 to 20, 24, 25, 28, 32 Register 21 Controller 22, 31, 36 Selector 23 Subtractor 26, 29 Adder 27, 30 Shifter

Claims (1)

A recording position control method for generating a timing signal that defines a driving timing of a recording element when performing recording by scanning a carriage equipped with a recording head having a recording element on a recording medium, comprising:
Measure the cycle of the rising and falling edges of the pulse signal output from the encoder according to the position of the carriage in the scanning direction,
The cycle of the timing signal is calculated by dividing the cycle of the edge by a predetermined number,
Updating the cycle of the timing signal based on the calculation result;
In the above calculation, the division is performed after adding the remainder generated in the previous calculation to the cycle of the edge.

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