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.*;


public class Contest {
    public static void main(String[] args) throws IOException{
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String[] input = in.readLine().split("\\s+");
        boolean[] flag = new boolean[100001];
        int a = Integer.parseInt(input[0]);
        int b = Integer.parseInt(input[1]);
        int c = Integer.parseInt(input[2]);
        int count = 0,result=-1;
        int res = a%b;
        while(res!=0 && flag[res]==false){
            flag[res]=true;
            count++;
            res*=10;
            if((res/b)==c){
                result = count;
                break;
            }
            res = res%b;
        }
        if(res==0 && c==0)
            result=count+1;
        System.out.println(result);
    }
}

