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.io.*;
import java.util.*;

public class B 
{
	public static void main(String[] args) throws Exception 
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
	
		int a = sc.nextInt() , b = sc.nextInt() , c = sc.nextInt();
		TreeSet<Integer> set = new TreeSet<>();
		
		for( int idx = 1; !set.contains(a) ; idx++)
		{
			set.add(a);
			
			a *= 10 ; 
			
			if(a / b == c)
			{
				System.out.println(idx);
				return ;
			}
			
			a-= a / b  * b ;
		}
		
		out.println(-1);
		
		
		out.flush();
		out.close();

	}
	

}