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.math.BigDecimal;
import java.util.Scanner;
public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner input = new Scanner(System.in);
		while(input.hasNext()){
			BigDecimal a = input.nextBigDecimal();
			BigDecimal b = input.nextBigDecimal();
			int c = input.nextInt();
			BigDecimal d = a.divide(b,1000,BigDecimal.ROUND_DOWN);
			String s = String.valueOf(d);
			int result = -1;
			for(int i = 2;i < s.length();i++)
				if(s.charAt(i) - 48 == c){
					result = i - 1;
					break;
				}
			System.out.println(result);
		}
	}

}
