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 P150916_320C {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        double a = scanner.nextDouble();
        double b = scanner.nextDouble();

        double EPS = 1e-8;
        double result = 1e12;


        //left side
        double x = a - b;
        if (Math.abs(x) < EPS) result = Math.min(result, b);
        if (x > EPS) {
            double count = Math.floor(x / (2 * b)) * 2;
            double left = x - count * b;
            if (count > EPS) {
                result = Math.min(result, b + left / count);
            }

            count = Math.floor((a + b) / (2 * b)) * 2;
            left = a + b - count * b;
            result = Math.min(result, b + left / count);
        }

        if (result > 1e9)
            System.out.println(-1);
        else
            System.out.println(result);


    }

}