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:
// practice with rainboy
import java.io.*;
import java.util.*;

public class CF578A extends PrintWriter {
	CF578A() { super(System.out, true); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF578A o = new CF578A(); o.main(); o.flush();
	}

	void main() {
		int x = sc.nextInt();
		int y = sc.nextInt();
		if (x < y) {
			println(-1);
			return;
		}
		if (x == y) {
			println(y);
			return;
		}
		double z1 = (double) (x + y) / ((x + y) / (2 * y) * 2);
		double z2 = (double) (x - y) / ((x - y) / (2 * y) * 2);
		printf("%.9f\n", Math.min(z1, z2));
	}
}