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 zviad on 12/14/17.
 */
public class FindExtraOne {

    public static void main(String argv[]) {
//        File file = new File("src/test/resources/input.txt");
        Scanner scanner = new Scanner(System.in);
        int a=scanner.nextInt();
        int b=scanner.nextInt();
        int c=scanner.nextInt();

        int k=0;
        int dir=a/b,rem;
        rem=a-dir*b;
        while(  k<1000){
            rem*=10;
            k++;
            dir=rem/b;
            if(dir==c){
                System.out.println(k);
                return;
            }
            rem=rem-dir*b;
        }
        System.out.println(-1);




    }


}
