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.io.*;
import java.io.PrintWriter;
import java.util.*;
import java.io.InputStream;
import java.io.DataInputStream;
 
 
 
public class Main
{
  //static{ System.out.println("hello");}
        static InputStream inputStream = System.in;
        static OutputStream outputStream = System.out;
        static FastReader scn = new FastReader(inputStream);
        static PrintWriter out = new PrintWriter(outputStream);
        static int fibo[]=new int[61];
        static int start;
        static void print(int a[])
         {        for (int i=0;i<a.length ;i++)
               {
                    out.print(a[i]+" ");   
               }   
        }   
     
        public static void main(String[] args) throws IOException
       {  
           int a=scn.ni();
           int b=scn.ni();
           int sum=a+b;
           int diff=a-b;
           double min,min2;
          int k1=(a+b)/(2*b);
          int k2=(a-b)/(2*b);
          if (k1==0 && k2==0) out.println(-1);
          else  if (k1==0 && k2!=0) out.println((double)(a-b)/(2*k2) );
          else if (k1!=0 && k2==0) out.println((double)(a+b)/(2*k1) );
          else
          out.println(Math.min  ((double)(a+b)/(2*k1),(double)(a-b)/(2*k2) )        );
             out.close();
        }     
  
                    
         
}


  class num 
    {
        
        public int ff;
        public int ss;
   
        num()
        {
            
        }
        num(int x,int y)
        {
            this.ff = x;
            this.ss =y;
       
        }
        public int getff()
        {
        return ff;
        }
        public int getss()
        {
        return ss;
        }
       public boolean equals(Object n1)
        {num n=(num)n1;
        if (this.ff==n.ff && this.ss==n.ss) return true;
        else return false;
            
            
        }
    }

class FastReader
{
 
    public InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public FastReader(InputStream stream)
    {
        this.stream = stream;
    }
 
    public int read()
    {
        if (numChars == -1)
        {
            throw new InputMismatchException ();
        }
        if (curChar >= numChars)
        {
            curChar = 0;
            try
            {
                numChars = stream.read (buf);
            } catch (IOException e)
            {
                throw new InputMismatchException ();
            }
            if (numChars <= 0)
            {
                return -1;
            }
        }
        return buf[curChar++];
    }
    
 public char nc()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        return (char) c;
    }
    
    public int ni()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read ();
        }
        int res = 0;
        do
        {
            if (c < '0' || c > '9')
            {
 
                
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }
 
    public long nl()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read ();
        }
        long res = 0;
        do
        {
            if (c < '0' || c > '9')
            {
                throw new InputMismatchException ();
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }
 
    public String ns()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        StringBuilder res = new StringBuilder ();
        do
        {
            res.appendCodePoint (c);
            c = read ();
        } while (!isSpaceChar (c));
        return res.toString ();
    }
 
    public boolean isSpaceChar(int c)
    {
        if (filter != null)
        {
            return filter.isSpaceChar (c);
        }
        return isWhitespace (c);
    }
 
    public static boolean isWhitespace(int c)
    {
        return c==' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next()
    {
        return ns ();
    }
 
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}