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

public class Problem900B {
public static void main(String args[]) throws IOException {
        Scanner sc = new Scanner(System.in);
        
        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();
        
        
        int f = 0;
        
        for(int i = 1; i < 200000; i++) {
                if((a*10) / b == c) {
                        System.out.println(i);
                        f = 1;
                        break;
                }
                
                a = (a*10)%b;
        }
        if(f == 0)
        System.out.println("-1");
        
}
}