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;

/**
 * Created by IntelliJ IDEA.
 * User: Enmanuel Reyes
 * Date: 12/11/17
 * Time: 1:07 PM
 * <p>
 * http://codeforces.com/contest/900/problem/B
 */
public class PositionFraction {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();
        a %= b;
        boolean found = false;
        for (int i = 1; i <= 200000; i++) {
            a *= 10;
            if (a/b == c) {

                found = true;
                System.out.println(i);
                break;
            }
            a %= b;
        }

        if (!found)
            System.out.println(-1);


    }
}
