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.Scanner;

public class test {
	public static void main(String[] args) {
	
		Scanner in=new Scanner(System.in);
		
		long a=in.nextLong();
		long b=in.nextLong();
		
		if(a<b)
			System.out.println("-1");
		else {
			Long d=(a-b)/(2*b);
			double e=(double)((a-b))/(2*d);
			double f=(double)((a+b))/(2*(d+1));
			if(a<3*b)
				System.out.println(f);
			else
				System.out.println((Math.min(e, f)));
		}
	}
}