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.math.BigDecimal;
import java.util.Scanner;


public class Main {
   
	 public static BigDecimal bigDiv(String v1, String v2, int scale) {   
	        BigDecimal b1 = new BigDecimal(v1);   
	        BigDecimal b2 = new BigDecimal(v2);   
	        return b1.divide(b2, scale, BigDecimal.ROUND_HALF_UP);   
	    }   
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner cin=new Scanner(System.in);
		while(cin.hasNext())
		{	
			double a=cin.nextDouble();
			double b=cin.nextDouble();
			int c=cin.nextInt();
			String temp1=Double.toString(a);
			String temp2=Double.toString(b);
			BigDecimal ans=bigDiv(temp1,temp2,10000);
			//System.out.println(ans);
			int flag=0;
			String s=ans.toString();
			int i;
			for(i=2;i<10000;i++)
			{
				if(s.charAt(i)-'0'==c)
				{
					flag=1;
					break;
				}
			}
			if(flag==1)
				System.out.println(i-1);
			else 
				System.out.println("-1");
		}
	}

}
