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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class WithIndex<T>
{
    public T Value;
    public int Index;
    public WithIndex(T value, int index)
    {
        this.Value = value;
        this.Index = index;
    }
}

static class Template
{
    public static int LineToInt()
    {
        return int.Parse(Console.ReadLine());
    }

    public static string[] LineToStrings()
    {
        return Console.ReadLine().Split();
    }

    public static int[] LineToInts()
    {
        return LineToStrings()
            .Select(s => int.Parse(s))
            .ToArray();
    }


    public static int[,] LinesToIntTable(int lineCount, int columnCount)
    {
        var value = new int[lineCount, columnCount];
        foreach (var y in Enumerable.Range(0, lineCount))
        {
            var ints = LineToInts();
            foreach (var x in Enumerable.Range(0, columnCount))
            {
                value[y, x] = ints[x];
            }
        }
        return value;
    }

    public static IEnumerable<WithIndex<T>> WithIndex<T>(this IEnumerable<T> sequence)
    {
        int index = 0;
        foreach (var item in sequence)
        {
            yield return new WithIndex<T>(item, index);
            index++;
        }
    }

    static void Main(string[] args)
    {
        var inputs = LineToInts();
        var n = inputs[0];
        var r = inputs[1];
        var count = 1;
        var i = r + 1;
        while (i + r + 1 <= n)
        {
            count++;
            i += 2 * r + 1;
        }
        Console.WriteLine(count);
    }
}