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. 
from sys import stdin, stdout

a, b, c = map(int, stdin.readline().split())
sze = 10 ** 5
used = set()

for i in range(1, sze + 1):
    cur = (a * 10) // b
    a = (a * 10) % b
    
    if cur == c:
        stdout.write(str(i))
        break
    
    if a in used:
        stdout.write('-1')
        break    
    
    used.add(a)
    
else:
    stdout.write('!')