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 Test665f {
	
	static final double sqrt2 =  Math.sqrt(2);

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		

		Scanner in = new Scanner(System.in);
		long x = in.nextInt();
		long y = in.nextInt();

		if (x < y) {
			System.out.println(-1);
			return;
		}
		if (x == y) {
			System.out.println(x);
			return;
		}

		double val1 = ((x + y)/ (2.0*y));
		double res1 = ((x+y)/sqrt2) / ((long) val1);
		double res1fin= res1/sqrt2;

		double val2 = ((x - y)/ (2.0*y));
		double res2 = ((x-y)/sqrt2) / (long)val2;
		double res2fin= res2/sqrt2;

		System.out.println(Math.min(res1fin, res2fin));

	}

}