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:
//package codeforces;
import java.util.*;
public class J578A {
	public static void main(String[] args) throws Exception
	{
		Scanner cin=new Scanner(System.in);
		double a=cin.nextDouble(),b=cin.nextDouble();
		double ans=1e18;
		if ((a+b)/2/b>=1)
		{
			double k=Math.floor((a+b)/2/b);
			if (k>0)
				if ((a+b)/2/k<ans) ans=(a+b)/2/k;
		}
		if ((a-b)/2/b>=1)
		{
			double k=Math.floor((a-b)/2/b);
			if (k>0)
				if ((a-b)/2/k<ans) ans=(a-b)/2/k;
		}
		if (ans==1e18)
			System.out.print("-1");
		else
			System.out.printf("%.9f",ans);
		cin.close();
	}
}