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 C {
    static int a, b;

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

        a = cin.nextInt();
        b = cin.nextInt();
        cin.close();

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

        int x = a + b;
        int steep = x / (2 * b);
        if (x % (2 * b) == 0) {
            System.out.println(b);
        } else {
            System.out.println(((double) x) / ((double) 2 * steep));
        }
    }
}