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 PositionInFraction {
	
		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);
		}
}
