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.Scanner;

public class B {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int a, b, c;
		a = in.nextInt();
		b = in.nextInt();
		c = in.nextInt();
		int ans = 1 ;
		for(int i = 0 ; i < 100000 ; i++){
			a*=10;
			int temp = a/b;
			if(temp==c){
				System.out.println(ans);
				return;
			}
			a%=b;
			ans++;
		}
		System.out.println(-1);
	}

}
