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 Second {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int a,b,c,div,pos=0;
		Scanner sc = new Scanner(System.in);
		a = sc.nextInt();
		b = sc.nextInt();
		c = sc.nextInt();
		int rem = a%b;
		
		while(pos<100000){
			rem = rem*10;
			div = rem / b;
			rem = rem % b;
			pos++;
			if(div == c){
				break;
			}
		}
		if(pos==100000 ){
			System.out.println("-1");
		}
		else{
			System.out.println(pos);
		}
		
	}

}
