The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 181 (Div. 2) |
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Finished |

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brute force

combinatorics

*1800

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C. Beautiful Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

stdinoutput

stdoutVitaly is a very weird man. He's got two favorite digits *a* and *b*. Vitaly calls a positive integer good, if the decimal representation of this integer only contains digits *a* and *b*. Vitaly calls a good number excellent, if the sum of its digits is a good number.

For example, let's say that Vitaly's favourite digits are 1 and 3, then number 12 isn't good and numbers 13 or 311 are. Also, number 111 is excellent and number 11 isn't.

Now Vitaly is wondering, how many excellent numbers of length exactly *n* are there. As this number can be rather large, he asks you to count the remainder after dividing it by 1000000007 (10^{9} + 7).

A number's length is the number of digits in its decimal representation without leading zeroes.

Input

The first line contains three integers: *a*, *b*, *n* (1 ≤ *a* < *b* ≤ 9, 1 ≤ *n* ≤ 10^{6}).

Output

Print a single integer — the answer to the problem modulo 1000000007 (10^{9} + 7).

Examples

Input

1 3 3

Output

1

Input

2 3 10

Output

165

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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