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 Temp3
{
	public static void main(String[] args) 
	{
		Scanner obj = new Scanner(System.in);
		int a = obj.nextInt();
		int b = obj.nextInt();
		int c = obj.nextInt();
		
		for(int i=1 ; i<=b ; i++)
		{
			int num = a*10/b;			
			if(num==c)
			{
				System.out.println(i);
				return;
			}			
			a = (a*10)%b;
		}
		
		System.out.println(-1);
	}
}