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 Hado0o0l
 */
public class Jamprograming {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here


        
Scanner input=new Scanner (System.in);

int i1=input.nextInt();
int i2=input.nextInt();
int i3=input.nextInt();

for(int i = 1; i < 300; i++) {  
            i1 *= 10;  
            if(i1/i2==i3) {  
                System.out.println(i);
                break;  
            }  
            i1 =i1%i2;
            if(i == 299)
                System.out.println(-1);
}
           
    }}
