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 Solution {
    public static int getPosition(int a, int b, int c){
        int ans = -1;

        for (int i = 1; i < 10000; i++){
            a *= 10;

            if(a / b == c){
                ans = i;
                break;
            }

            a %= b;
        }
        return ans;
    }

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);

        int a = scan.nextInt();
        int b = scan.nextInt();
        int c = scan.nextInt();

        System.out.println(getPosition(a, b, c));
    }
}

	 	 			 		   		 				  	   		 	