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. 
//package codeforces;
import java.util.*;
public class PositioninFraction {

	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int a,b,c,i;
		a=in.nextInt();b=in.nextInt();c=in.nextInt();
		int value,flag=0;
		for(i=1;i<=b;i++)
		{
			a*=10;
			value=a/b;
			a=a%b;
			if(value==c){flag=1;System.out.println(i);break;}
		}
		if(flag==0)System.out.println(-1);
	}

}
