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 z_8 {
    public static void main(String[] args) {
	Scanner lector = new Scanner(System.in);
 
	int a = lector.nextInt();
	int b = lector.nextInt();
	int c = lector.nextInt();
	System.out.println(solve(a, b, c));
 
	lector.close();
    }
 
    static int solve(int a, int b, int c) {
	boolean[] seen = new boolean[b];
	int residuo = a;
	int result = 1;
	while (true) {
	    int digit = residuo * 10 / b;
	    if (digit == c) {
		return result;
	    }
 
	    residuo = residuo * 10 % b;
	    if (seen[residuo]) {
		return -1;
	    }
 
	    seen[residuo] = true;
	    result++;
	}
    }
}