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.Scanner;

/**
 *
 * @author bashayrhindi
 */
public class MainClass {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
    Scanner in=new Scanner(System.in);
        int n=in.nextInt();
        int o=in.nextInt();
        int p=in.nextInt();

        for (int i = 1; i < 300; i++) {
            n=n*10;
            if(n/o==p){System.out.println(i);break;}
            n=n%o;
            if(i==299)System.out.println("-1");
        }
    
    }
    

}
