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. 
import bisect

def list_output(s):    
    print(' '.join(map(str, s)))
    
def list_input(s='int'):
    if s == 'int':
        return list(map(int, input().split()))    
    elif s == 'float':
        return list(map(float, input().split()))
    return list(map(str, input().split()))

[a, b, c] = list(map(int, input().split()))
cnt = 1
for _ in range(1000000):
    a *= 10
    d = a//b
    r = a%b
    if d == c:
        print(cnt)
        exit(0)
    a = r
    cnt += 1
print(-1)

