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;

/**
 * Created by tignatchenko on 16.09.2015.
 */
public class z3 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int b = sc.nextInt();
        if (a<b) {
            System.out.println(-1);
        } else {
            int k1 = (int)Math.floor((double)(a-b)/(2*b));
            int k2 = (int)Math.floor((double)(a+b)/(2*b)-1);
            double m = (double)(a+b)/(2*(k2+1));
            double n = (double)(a-b)/(2*k1);

            if (k1<=0 && k2<0) {
                System.out.println(-1);
            } else if (k1<=0) {
                System.out.println(m);
            } else if (k2<0) {
                System.out.println(n);
            } else{
                System.out.println(Math.min((double)(a+b)/(2*(k2+1)), (double)(a-b)/(2*k1)));
            }

        }
    }
}