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.*;
import java.math.*;

public class Main {
	public static void main(String args[])
	{
		Scanner in=new Scanner(System.in);
		int a,b;int flag=-1;
		String c;
		a=in.nextInt();
		b=in.nextInt();
		c=in.next();
		if(a>b)a=a%b;
		BigDecimal A=new BigDecimal(Integer.toString(a));
		BigDecimal B=new BigDecimal(Integer.toString(b));
		String n=A.divide(B,100001,BigDecimal.ROUND_DOWN).toString();
		for(int i=2;i<n.length();i++)
		{
			if(n.charAt(i)==c.charAt(0))
			{
				flag=i-1;
				break;
			}
		}
		System.out.println(flag);
		in.close();
	}
}
