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.Formatter;
import java.util.Scanner;
import java.math.*;

public class Fraction {

	static Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		
		int a,b;
		int c;
		double d;
		a = sc.nextInt();
		b=sc.nextInt();
		c=sc.nextInt();
		long i = 0;
		while(i++<10000000)
		{
			a= a*10;
			if((a/b)==c)
			{
				System.out.println(i);
				break;
			}
			a=a%b;
		}
		if(i==10000001)
			System.out.println(-1);
		
		
	}

}
