Educational Codeforces Round 8 |
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Finished |

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D. Magic Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputConsider the decimal presentation of an integer. Let's call a number d-magic if digit *d* appears in decimal presentation of the number on even positions and nowhere else.

For example, the numbers 1727374, 17, 1 are 7-magic but 77, 7, 123, 34, 71 are not 7-magic. On the other hand the number 7 is 0-magic, 123 is 2-magic, 34 is 4-magic and 71 is 1-magic.

Find the number of d-magic numbers in the segment [*a*, *b*] that are multiple of *m*. Because the answer can be very huge you should only find its value modulo 10^{9} + 7 (so you should find the remainder after dividing by 10^{9} + 7).

Input

The first line contains two integers *m*, *d* (1 ≤ *m* ≤ 2000, 0 ≤ *d* ≤ 9) — the parameters from the problem statement.

The second line contains positive integer *a* in decimal presentation (without leading zeroes).

The third line contains positive integer *b* in decimal presentation (without leading zeroes).

It is guaranteed that *a* ≤ *b*, the number of digits in *a* and *b* are the same and don't exceed 2000.

Output

Print the only integer *a* — the remainder after dividing by 10^{9} + 7 of the number of d-magic numbers in segment [*a*, *b*] that are multiple of *m*.

Examples

Input

2 6

10

99

Output

8

Input

2 0

1

9

Output

4

Input

19 7

1000

9999

Output

6

Note

The numbers from the answer of the first example are 16, 26, 36, 46, 56, 76, 86 and 96.

The numbers from the answer of the second example are 2, 4, 6 and 8.

The numbers from the answer of the third example are 1767, 2717, 5757, 6707, 8797 and 9747.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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