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. 


def Decimals(a, b):
    denom = list()
    while a != 0 and a not in denom:
        denom.append(a)
        a *= 10
        yield a // b
        a = a % b
    if a == 0:
        yield 0
        


def main():
    a, b, c = map(int, input().strip().split())

    for (i, n) in enumerate(Decimals(a, b)):
        if n == c:
            print(i + 1)
            return
    else:
        print(-1)



if __name__ == "__main__":
    main()
