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 ProblemPolyline {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int b = sc.nextInt();
        double result = -1;
        if (a == b) {
            result = a;
        } else if (a > b) {
            int k = (a / b + 1) / 2;
            result = 1.0 * (a + b) / (2 * k);

            int k2 = (a / b - 1) / 2;
            double result2 = 1.0 * (a - b) / (2 * k2);

            result = Math.min(result, result2);
        }
        System.out.format("%.10f", result);
    }
}