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.math.BigDecimal;
import java.util.Scanner;

/**
 *
 * @author Tomás
 */
public class JavaApplication1 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        BigDecimal bd, a, b;
        int c, index;
        Scanner scanner = new Scanner(System.in);
        
        a = BigDecimal.valueOf(scanner.nextInt());
        b = BigDecimal.valueOf(scanner.nextInt());
        c = scanner.nextInt();
        
        bd = a.divide(b, 100005, BigDecimal.ROUND_FLOOR);
        String ts = bd.toString();
        
        index = bd.toString().split("\\.")[1].indexOf(c + "");
        if(index == -1)
            System.out.println("-1");
        else
            System.out.println(index + 1);
    }
}
