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 AProblemAboutPolyline {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int x = sc.nextInt(), y = sc.nextInt();
		if (y > x) {
			System.out.println(-1);
		} else {
			double c = y + x;
			double ret = c / 2;
			long k = (long) Math.floor(ret / (double) y);
			System.out.println(ret / k);
		}
	}

}