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():
    a, b, c = map(int, input().split())
    a %= b
    a += b
    if a == 0:
        if c == 0:
            print(1)
        else:
            print(-1)
        exit(0)
    a = str(a * (10 ** 100000) // b)
    for i in range(1, len(a)):
        if int(a[i]) == c:
            print(i)
            exit(0)
    print(-1)


main()