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.io.*;

public class Main {
  public static void main (String[] args) {
    Scanner sc = new Scanner(System.in);
    //BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    double a = sc.nextInt();
    double b = sc.nextInt();
    int c = sc.nextInt();
    double quo = a/b;
//     System.out.println(quo);
    boolean[] rems = new boolean[(int)b];
    Arrays.fill(rems, false);
    int aS = (int)a*10;
    String s = "";
    int ans = -1;
    int count = 0;
    while(true) {
      if(s.length() > 0 && Integer.parseInt(s.charAt(s.length()-1)+"") == c) {
        ans = count;
        break;
      }
      else if(aS == 0){
        if(c == 0)
          ans = count+1;
        break;
      }
      if(aS < b) {
        aS *= 10;
        s += "0";
      }
      else {
        int rem = aS % (int)b;
//         System.out.println(rem);
        if(rems[rem]) {
          break;
        }
        else {
          s += (aS / (int)b);
          aS = rem;
          rems[rem] = true;
          aS *= 10;
        }
      }
//       System.out.println("String: " + s);
      count++;
    }
    
    System.out.println(ans);
  }
}
