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.*; 
public class posiC{
 public static void main(String[] args) {
        // TODO code application logic here
 
        Scanner input = new Scanner(System.in);
        int a, b, c = 0;
        a = input.nextInt();
        b = input.nextInt();
        c = input.nextInt();
        System.out.println(position(a, b, c));  
 
    }
 
    public static int position(int a, int b, int c) {
 
        a %= b;
 
        for (int i = 1; i <= b; i++) {
 
            a = a * 10;
 
            if (a / b == c) {
                return i;
            }
 
            a %= b;
 
        }
        return -1;
    }}