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 main():
    was = [False] * 1000005
    a, b, c = map(int, input().split())
    p = 0
    while True:
        p += 1
        a *= 10
        if was[a]:
            break
        was[a] = True
        cur = int(a / b)
        a %= b
        if cur == c:
            print(p)
            return
    print(-1)
        

if __name__ == '__main__':
    # print(int(2/3))
    main()