You have a fraction <image>. You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.

Input

The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).

Output

Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.

Examples

Input

1 2 0


Output

2

Input

2 3 7


Output

-1

Note

The fraction in the first example has the following decimal notation: <image>. The first zero stands on second position.

The fraction in the second example has the following decimal notation: <image>. There is no digit 7 in decimal notation of the fraction. 
# https://codeforces.com/problemset/problem/900/B

import sys
import math


def main():
    # sys.stdin = open('E:\\Sublime\\in.txt', 'r')
    # sys.stdout = open('E:\\Sublime\\out.txt', 'w')
    # sys.stderr = open('E:\\Sublime\\err.txt', 'w')

    # n = int(sys.stdin.readline().strip())
    a, b, c = map(int, sys.stdin.readline().strip().split())

    for i in range(b):
        a *= 10
        pos = a // b
        a = a % b
        if c == pos:
            print((i + 1))
            return 0
    print(-1)


if __name__ == '__main__':
    main()

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# 　＼二つ
