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.math.RoundingMode;
import java.util.Scanner;

public class Main
{
    public static void main(String[] args)
    {
        Scanner sc = new Scanner(System.in);
        BigDecimal a = sc.nextBigDecimal(), b = sc.nextBigDecimal();
        String c = sc.next();
        a = a.divide(b, 200000, RoundingMode.HALF_UP);
        String s = a.toString();
        s =  s.substring(0, 150000);
        int ans = -1;
        boolean f = false;
        for(int i = 0; i < s.length(); i++)
        {
            if(s.charAt(i) == '.')
            {
                f = true;
            }

            if(f) ++ans;
            if(f && s.charAt(i) == c.charAt(0))
            {
                System.out.println(ans);
                System.exit(0);
            }
        }
        
        System.out.println("-1");
    }
}
