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 java.util.*;
public class duh {
    public static void main(String[] args) {
        Scanner ob=new Scanner(System.in);
        int a=ob.nextInt();
        int b=ob.nextInt();
        int c=ob.nextInt();
        a*=10;
        Set<Integer> set=new TreeSet<>();
        int rem=a%b,pos=0,flag=0,x=a/b;
        while(true)
        {
            pos++;
            if(x==c)
            {flag=1;break;}
            if(set.contains(rem))
            break;
            set.add(rem);
            rem*=10;
            x=rem/b;
            rem=rem%b;
        }
        if(flag==1)
            System.out.print(pos);
        else System.out.print(-1);
    }
    }


