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 Prob2 {

public static void main(String[] args) {
		
		
		Scanner scanner = new Scanner(System.in);
		int a = scanner.nextInt();
		int b = scanner.nextInt();
		int c = scanner.nextInt();
	
		
		int temp = 0;
		int remainder = 0;
		int n = 0;
	
		int count = 1;
		boolean found = false;
	
		while(n < 10000){
			
			temp = a * 10 / b;
			if (temp == c){
				found = true;
				break;
			}
			
			
			a = (a*10)% b;
			count++;
			n++;
		}
		
		if(found){
			System.out.println(count);
		}
		else{
			System.out.println(-1);
		}
		
		
		
	}
}
