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.*;
import java.util.*;

public class Codeforces900B {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sp = br.readLine().split(" ");
		int a = Integer.parseInt(sp[0]);
		int b = Integer.parseInt(sp[1]);
		int c = Integer.parseInt(sp[2]);
		a = a%b;
		
		boolean bool = true;
		int counter = 0;
		int quot = (10*a)/b;
		a = (10*a)%b;
		counter = 1;
		while ((counter < 200000) && bool) {
			if (quot == c) {
				bool = false;
			}
			else {
				quot = (10*a)/b;
				a = (10*a)%b;
				counter++;
			}
		}
		if (bool) {
			System.out.println(-1);
		}
		else {
			System.out.println(counter);
		}
	}
}
