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 long_div(a, b):
    remain = {}
    a *= 10
    # print(a, "div", b)
    while a not in remain:
        remain[a] = True
        d = a // b
        r = a % b
        a = r * 10
        # print("digit:", d, "remain:", r)
        yield d
    # print(remain)

def solution(a, b, c):
    for i, d in enumerate(long_div(a, b)):
        if d == c:
            return i + 1
    return -1
if __name__ == "__main__":
    a, b, c = map(int, input().split())
    print(solution(a, b, c))
