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 static java.lang.Math.*;
import java.io.*;

public class SolutionB {
       
      public static void main(String args[])throws IOException{
              Scanner sc = new Scanner(System.in);
              int a = sc.nextInt();
              int b = sc.nextInt();
              int t = sc.nextInt();
              String aa = String.valueOf(a);
              String bb = String.valueOf(b);
             // System.out.println(aa);
              //System.out.println(bb);
              boolean divide = true;
              int i = 0;
              StringBuilder sb = new StringBuilder();
              int curr = 0;
              int last = -1;
              int cnt = 0;
              while(divide){
                     if(curr < b){
                            if(i < aa.length()){
                                   curr *= 10;
                                   curr += (aa.charAt(i++) - '0');
                                   if(curr >= b){
                                          sb.append((curr / b));
                                          curr = curr - (curr/b)*b;
                                   }
                            }else{
                                   if(i == aa.length()){
                                          i++;
                                          sb.append('.');
                                   }
                                   last = curr;
                                   curr *= 10;
                                   cnt++;
                                   sb.append((curr/b));
                                   if((curr/b) == t){
                                          System.out.println(cnt);
                                          break;
                                   }
                                   curr = curr - (curr/b)*b;
                            }
                     }
                     if((curr == 0 && i >= aa.length()) || last == curr || cnt > 10000){
                                   divide = false;
                                   if(t == curr){
                                          System.out.println(++cnt);
                                   }else{
                                          System.out.println(-1);
                                   }
                                   
                     }
                    // System.out.println(sb.toString());
              }
      }
}