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.io.*;

public class CExp
{
   public static void main(String[] args)
   {
      MyScanner scan = new MyScanner();
      
      
      double a = scan.nextDouble();
      double b = scan.nextDouble();
      
      boolean flag = false;
      int left = 0; 
      int right = (int)a;
      double bestX = -1;
      while(right>left+1)
      {
         int mid = (left+right)/2;
         if(mid == left)
         {
            mid++;
         }
         
         double x;
         if(mid%2 == 0)
         {
            x = (a-b)/mid; 
         }
         else
         {
            x = (a+b)/(mid+1);
         }
         if(b <= x)
         {
            bestX = x;
            left = mid;
         }
         else
         {
            right = mid;
         }
      }
      
      if(bestX == -1)
      {
         System.out.println(bestX);
      }  
      else
      {
         System.out.printf("%.9f", bestX);
      }
   }
      
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
   
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
   
      String next() {
         while (st == null || !st.hasMoreElements()) {
            try {
               st = new StringTokenizer(br.readLine());
            } 
            catch (IOException e) {
               e.printStackTrace();
            }
         }
         return st.nextToken();
      }
   
      int nextInt() {
         return Integer.parseInt(next());
      }
   
      long nextLong() {
         return Long.parseLong(next());
      }
   
      double nextDouble() {
         return Double.parseDouble(next());
      }
   
      String nextLine() {
         String str = "";
         try {
            str = br.readLine();
         } 
         catch (IOException e) {
            e.printStackTrace();
         }
         return str;
      }
   }
}