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.util.Scanner;

public class Polyline {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        
        Scanner c = new Scanner(System.in);
        double a = c.nextDouble();
        double b = c.nextDouble();
               
        double center = Math.max(a - b, b + a);
        double t = center/b;
        int times = (int)t/2;
        if(times <= 0) {
            System.out.println(-1);
            return;
        }
        double res = (center/times)/2; 
        
        if (res < b) {
            System.out.println(-1);
        }
        else System.out.println(res);
            
    }
    
}