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:
//package CodeForces.Ternar;

import java.util.Scanner;

public class Task578A {
    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        double x = scn.nextInt();
        double y = scn.nextInt();
        if(y>x){
            System.out.println(-1);
            return;
        }
        if(y==x){
            System.out.println(y);
            return;
        }
        double res;
        double a = x-y;
        double min = y*2;
        res=a/(double)((int)a/(int)min)/2;
        a=x+y;
        res=Math.min(res, a/(double)((int)a/(int)min)/2);
        System.out.println(res);
    }
}