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.*;
import java.util.*;

public class CF320C {
    
    public static void main(String[] args) {
      
        Scanner sc = new Scanner(System.in);  
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
     
        int x = sc.nextInt();
        int y = sc.nextInt();
        
        double x1 = x;
        double y1 = y;
        
        if (y > x) {
            out.println("-1");
        } else {
            double i1 = Math.floor((x1-y1)/2.0/y1);
            double a1 = 0;
            if (i1>0.0) {
                a1 = (x1-y1)/2.0/i1;
            }
            double i2 = Math.floor((x1+y1)/2.0/y1);
            double a2 = (x1+y1)/2.0/i2;
            if (i1>0.0 && a1<a2) {
                out.println(a1);
            } else {
                out.println(a2);
            }
        }

        out.close();
    }
}