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 = list(map(int, input('').strip().split()))
occur = dict()
count = 0
for i in range(10 ** 6):
    count += 1
    a *= 10
    occurs = a // b
    occur[a] = occurs
    left = a % b
    if occurs == c:
        print(count)
        break
    else:
        if left * 10 in occur:
            print(-1)
            break
        else:
            a = a % b