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.*;
import java.lang.*;
import java.io.*;
import java.util.ArrayList;
import java.util.Scanner;
 
 
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int a, b, c, q = 1;
    	a = sc.nextInt();
    	b = sc.nextInt();
    	c = sc.nextInt();
    	 while(q < 1000005){
    	   a *= 10;
            if(a/b == c){
              System.out.println(q);
              System.exit(0);
            }
         a %= b;
         q++;
    }
    System.out.print("-1");
	}
}