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 Solution {

    public static void main(String args[]){
        Scanner in=new Scanner(System.in);
        int a=in.nextInt(),b=in.nextInt();
        double ans;
        if(a==b)
            ans=a;
        else if(a<b)
            ans=-1;
        else{
            int c=a-b,d=a+b;
            int n1=c/b;
            int n2=d/b;
            n1=n1-(n1%2);
            n2=n2-(n2%2);
            ans=Math.min((double)c/n1, (double)d/n2);
        }
        if(ans!=-1)
            System.out.println(String.format("%.9f", ans));
        else
            System.out.println("-1");
        in.close();
    }
}