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 Main
{
     public static void main(String args[])
     {
          Scanner sc = new Scanner(System.in);
          int a = sc.nextInt();
          int b = sc.nextInt();
          int c = sc.nextInt();
          int flag = 0;
          for(int i=1;i<=b;i++)
          {
               a*=10;
               int val = a/b;
               a%=b;
               if(val==c)
               {
                    flag=1;
                    System.out.println(i);
                    break;
               }
          }
          if(flag==0)
          {
               System.out.println("-1");
          }
     }
}