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 = [int(i) for i in input().split()]
fr = [0] * 5000001
cr = a
ans = []
while cr < b:
    cr *= 10
    ans.append(0)
ans = ans[1:]
while True:
    fr[cr] = 1
    v = cr // b
    ans.append(v)
    cr = cr - v * b
    cr *= 10
    if fr[cr]:
        break
if c not in ans:
    print(-1)
else:
    print(ans.index(c) + 1)
