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;

public class Partition {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int a=input.nextInt(),b=input.nextInt(),c=input.nextInt(),i=1,c1=0;
        int x=a%b;
        while(true) {
           
            x=x*10;
            int x1=x/b;//by this operation i get the integer after the decimal point 
            if(x1==c){
                System.out.println(i);
                c1++;
                break;
            }else if( i==100000){
                break;
            }
            x=x%b;
            i++;
        }
        if(c1==0){
            System.out.println("-1");
        }
        
    }
}
