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. 
from decimal import *

def main():
    getcontext().prec = 500
    a, b, c = map(int, input().split())
    d = str(Decimal(a) / Decimal(b))
    d += "0" * (502 - (len(d)))
    cnt = [-2] * 10
    for idx, item in enumerate(d[2:-1]):
        if cnt[int(item)] == -2:
            cnt[int(item)] = idx
    print(cnt[c] + 1)


if __name__ == "__main__":
    main()
