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.*;
import java.text.*;
import java.lang.*;
public class Main
{
    static int p;
    static int q;
    static DecimalFormat df=new DecimalFormat("0.000000000000");
    public static void main(String[]args)
    {
        Scanner s=new Scanner(System.in);
        p=s.nextInt();
        q=s.nextInt();
        if(p<q)
        {
             System.out.println("-1");
        }
        else
        {
            double result=cal();
            System.out.println(df.format(result));
        }
    }
    static double cal()
    {
         if(p==q)
         {
              return (double)p;
         }
         else
         {
             double ref=(double)q;
             double d1=p-q;
             double d2=p+q;
             double d3=d1/(2.0*ref);
             double d4=d2/(2.0*ref);
             double result=min(d3,d4);
             int k=(int)(result);
             result=d2/(2*k);
             return result;
          }
    }
    static double min(double d1,double d2)
    {
          if(d1>=d2)
          {
             return d1;
          }
          else
          {
             return d2;
          }
    }
}