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 sys,math,string,bisect
input=sys.stdin.readline
from collections import deque
L=lambda : list(map(int,input().split()))
Ls=lambda : list(input().split())
M=lambda : map(int,input().split())
I=lambda :int(input())
a,b,c=M()
l=[0]*b
i=1
while(True):
    if((10*a)%b==0):
        if(c==0):
            print(i+1)
            exit()
    if(l[(10*a)%b]==0):
        
        l[(10*a)%b]+=1
        if(10*a)//b==c:
            print(i)
            exit()
        a=(10*a)%b

    elif(l[(10*a)%b]!=0):
        print(-1)
        exit()
    i+=1
    
