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 test4 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int x = sc.nextInt();
        int y = sc.nextInt();
        if(y > x) {
            System.out.println(-1);
            return;
        }
        if(y == x) {
            System.out.println(x);
            return;
        }

        double min = 2e9;
        double sum = (x+y)/2.0;
        double differ = (x-y)/2.0;

        double k1 = Math.floor((x-y)/2.0/y);
        double k2 = Math.floor((x+y)/2.0/y);

        while(differ >= y) {
            min = Math.min(min, differ);
            differ /= 2;
        }

        while(sum >= y) {
            min = Math.min(min, sum);
            sum /= 2;
        }
        double result = Math.min((x - y) / k1 / 2.0, (x + y) / k2 / 2.0);
        //System.out.printf("%.12f", min);
        //System.out.println();
        System.out.printf("%.12f", result);
    }
}