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. 
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
a,b,c=map(int,input().strip().split())
a=a%b
i=1
while i<100000:
    t=int((a*10)/b)
    if t==c:
        break
    a=a*10-(t*b)
    i+=1
    #print(t,a)
if i>=100000:
    print(-1)
else:
    print(i)