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[] str)
	{
		 Scanner cin=new Scanner(System.in);
		 int a1=cin.nextInt();
		 int b1=cin.nextInt();
		 String c=cin.next();
		 a1=a1%b1;
		 BigDecimal a,b;
		 a=BigDecimal.valueOf(a1);
		 b=BigDecimal.valueOf(b1);
		 a=a.divide(b, 1000, BigDecimal.ROUND_UP);
		 String d=a.toPlainString();
		 d=d.substring(1,900);
		 System.out.println(d.indexOf(c));
	}
}