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.*;

public class Main {
	public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int a = in.nextInt();
        int b = in.nextInt();

        if (a < b) {
            System.out.println(-1);
            return;
        }

        double answer = (a + b) / 2d;

        while (true) {
            int fold = (int) (answer / b);

            if (fold == 1) {
                break;
            }

            answer /= fold;
        }

        System.out.println(answer);
    }
}