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.Arrays;
import java.util.Scanner;


public class c {
    
   
    static int[][]a;
       public static void main(String[] args) {
        
          Scanner sc=new Scanner(System.in);
          
          int a=sc.nextInt();
          int b=sc.nextInt();
          
          
          if(a<b)
               System.out.println("-1");
    
          if(a==b)
               System.out.println(a);
          if(a>b)
          {
            int max = a + b;
            int div = max / ( 2 * b );
            System.out.println( 1.0 * max / 2 / div );
              
          }
       }
       
       
       
      
       
}