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. 

a, b, c = map(int, input().split())

a %= b

visited = set()

result = -1
i = 1

while True:
    if a * 10 in visited:
        break
    visited.add(a * 10)
    tmp = (a * 10) // b
    if tmp == c:
        result = i
        break
    a = (a * 10) % b
    i += 1


print(result)
