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.io.*;
import java.util.*;
public class chefexeq
{
    public static void main(String args[])throws IOException
    {
        Scanner in=new Scanner(System.in);
        double a=in.nextDouble();
        double b=in.nextDouble();
        int c=in.nextInt();
        int count=0;int flag=0;
        while(true)
        {
            double q=10*a;
            int num=(int)q/(int)b;
            //System.out.println(num);
            count++;
            if(num==c)
            break;
            a=q%b;
            if(count>1000000)
            {
                flag=1;
                break;
            }
        }
        if(flag==1)
        System.out.println(-1);
        else
        System.out.println(count);
    }
}