Problem: There is a polyline going through points (0, 0) – (x, x) – (2x, 0) – (3x, x) – (4x, 0) – ... - (2kx, 0) – (2kx + x, x) – .... 

We know that the polyline passes through the point (a, b). Find minimum positive value x such that it is true or determine that there is no such x.

Input

Only one line containing two positive integers a and b (1 ≤ a, b ≤ 109).

Output

Output the only line containing the answer. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9. If there is no such x then output  - 1 as the answer.

Examples

Input

3 1


Output

1.000000000000


Input

1 3


Output

-1


Input

4 1


Output

1.250000000000

Note

You can see following graphs for sample 1 and sample 3. 

<image> <image>

Solution (in JAVA):

Solution:
import java.io.PrintWriter;
import java.util.*;
import java.util.stream.IntStream;

import static java.lang.Math.*;

import static java.util.stream.IntStream.range;

public class Sub {

    public static void main(String[] args) throws Exception {
        new Sub().doit();
    }

    public void doit() throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int a = sc.nextInt();
        int b = sc.nextInt();

        if (a == b) {
            out.println(b);

        }
        else if (a < b) {
            out.println(-1);
        }
        else {


            int sum = a + b;

            long lo = 1; // one less than minimum
            long hi = 1000000000; // exactly max
            while(hi > lo+1) {
                long mid =  (lo+hi)/2;

                double cand = sum / (2. * mid);

                boolean inLower = false;
                if ( cand < b) {
                    inLower = true;
                }
            	if (inLower) // comparison function
            		hi = mid; // high sets <=
            	else
            		lo = mid; // low sets >
            }


            out.println( sum / (2. * lo)  );
            // sum = 2*y*x



        }
        // pick arbitrary a -> b
        


        sc.close();
        out.close();
    }

}