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.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
import java.util.Scanner;

public class BEddy1021 {

	public static void main(String[] args) {
		try (Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
				PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)))) {
			out.println(solve(in.nextInt(),in.nextInt(),in.nextInt()));
		}
	}

	private static int solve(int a,int b,int c) {
	    int ans = 1;
	    final Set<Integer> r=new HashSet<>();
	    a %= b;
	    a*=10;
	    while(!r.contains(a)){
	        if(a/b==c){
	            return ans;
	        }
	        ans++;
	        r.add(a);
	        a%=b;
	        a*=10;
	    }
	    return -1;
	}

}
