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.*;

public class a_problem_about_polyline
{
    public static void main( String[] args )
    {
        Scanner in = new Scanner( System.in );
        int a = in.nextInt(), b = in.nextInt();
        if ( a < b )
            System.out.println( -1 );
        else if ( a == b )
            System.out.println( a );
        else
        {
            int max = a + b;
            int div = max / ( 2 * b );
            System.out.println( 1.0 * max / 2 / div );
        }
        in.close();
        System.exit( 0 );
    }
}