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.PrintWriter;
import java.util.Scanner;

public class H {
 public static void main(String[] args) {
	 Scanner sc = new Scanner(System.in);
	 PrintWriter out = new PrintWriter(System.out);
	 int a = sc.nextInt(), b = sc.nextInt();
		if(b > a)
			out.println(-1);
		else
			if(a == b)
				out.println(a);
			else{
				double r = (a+b)/2.0;
				double r2 = (a-b)/2.0;
				double k = Math.floor((a+b)/(2.0*b));
				double k2 = Math.floor((a-b)/(2.0*b));
				out.println(Math.min(r/k, r2/k2));
 
			}
		out.close();
}
}