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. 
// In the name of Allah the Lord of the Worlds. 

import java.io.*;
import java.util.*;
import java.math.*;

public class Solution {
    
    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);     
        
        BigDecimal a = sc.nextBigDecimal();
        BigDecimal b = sc.nextBigDecimal();
        
        int x = sc.nextInt();
        
        a = a.divide(b , 3000 , BigDecimal.ROUND_HALF_UP);
        
        String ar = new String();
        ar = a.toPlainString();
        
        boolean check = false;
        
        ar+='0';
        int si = ar.length();
        
        int i = 0;
        int counter = 0;
        
        while(ar.charAt(i)=='0')i++;
        
        for(;i<Math.min(si,1000);i++){
            
            if(ar.charAt(i)!='.')counter++;
            
            if(ar.charAt(i)-'0'==x){
                
                check = true;
                System.out.println("" + (counter));
                break;
            }
        }
        
        if(check==false)System.out.println("-1");
    }
}