Problem:
Score : 200 points

Problem Statement

There are N apple trees in a row. People say that one of them will bear golden apples.

We want to deploy some number of inspectors so that each of these trees will be inspected.

Each inspector will be deployed under one of the trees. For convenience, we will assign numbers from 1 through N to the trees. An inspector deployed under the i-th tree (1 \leq i \leq N) will inspect the trees with numbers between i-D and i+D (inclusive).

Find the minimum number of inspectors that we need to deploy to achieve the objective.

Constraints

All values in input are integers.

1 \leq N \leq 20

1 \leq D \leq 20

Input

Input is given from Standard Input in the following format:

N D

Output

Print the minimum number of inspectors that we need to deploy to achieve the objective.

Sample Input 1

6 2

Sample Output 1

2

We can achieve the objective by, for example, placing an inspector under Tree 3 and Tree 4.

Sample Input 2

14 3

Sample Output 2

2

Sample Input 3

20 4

Sample Output 3

3

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

/*
Stay innocent, be naive. 
But still dream big. 
Dream big to the point that it is beyond your ability and endeavour to achieve it. 
So dream big and don�t lose your innocence.
*/
import java.util.*;
import java.io.*;

   public class Main
   {
      public static void main(String args[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         int D = Integer.parseInt(st.nextToken());
         int boof = 2*D+1;
         int res = N/boof;
         if(N%boof > 0)
            res++;
         System.out.println(res);
      }
      public static void sort(int[] arr)
      {
         //stable heap sort
         PriorityQueue<Integer> pq = new PriorityQueue<Integer>();
         for(int a: arr)
            pq.add(a);
         for(int i=0; i < arr.length; i++)
            arr[i] = pq.poll();
      }
   }