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 Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int a = scanner.nextInt(), b = scanner.nextInt();
        if (b > a) {
            System.out.println(-1);
            return;
        }
        if (a == b) {
            System.out.println(a);
            return;
        }
        double n1 = Math.ceil((a - b) / 2 / b);
        double x1 = (a - b) / n1 / 2;
        double n2 = Math.ceil((a + b) / 2 / b);
        double x2 = (a + b) / n2 / 2;
        System.out.println(Math.min(x1, x2));
    }
}