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.io.*;
import java.util.*;
import java.math.BigInteger;
import java.math.BigDecimal;
import java.math.RoundingMode;
public class forces{
    public static void main(String args[])throws IOException{
        DataInputStream ins=new DataInputStream(System.in);
		String abc[]=ins.readLine().split(" ");
		int a=Integer.parseInt(abc[0]);
		int b=Integer.parseInt(abc[1]);
		int c=Integer.parseInt(abc[2]);
		
		int scale = 10000;
		BigDecimal num1 = new BigDecimal(a);
		BigDecimal num2 = new BigDecimal(b);
		String show=num1.divide(num2, scale, RoundingMode.HALF_UP).toString();
		//System.out.println(show);
		show=show.substring(show.indexOf(".")+1, show.length()-1);
		int ind=show.indexOf(String.valueOf(c));
		if(ind>=0){
			System.out.println(ind+1);
		}
		else{
			System.out.println(-1);
		}
    }
}
