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 Solution
{
    public static void main(String[] args) 
    {
        Scanner in = new Scanner(System.in);
        String a = in.next();
        int b = in.nextInt();
        int c = in.nextInt();
        int count = 0;
        boolean not = false;
        for(int i=0;i<100000;i++)
        {
            a = a + "0";
            count++;
            //System.out.println(a);
            int temp = Integer.parseInt(a);
            int d = temp/b;
            int f = temp%b;
            a = Integer.toString(f);
            int last = d;
            //System.out.println(a + " " + d + " " + f);
            if(d == c)
            {
                not = true;
                break;
            }
        }
        if(not)
            System.out.println(count);
        else
            System.out.println("-1");
    }
}
