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.*;
import java.lang.*;
import java.io.*;

public class A
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner scan = new Scanner (System.in);
		int a = scan.nextInt(), b = scan.nextInt();
		if(b>a)System.out.println(-1);
		else{
			System.out.println((a+b)/(2.0*Math.floor((a*1.0+b)/(2.0*b))));
		}
		
	}
}