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;
using System.Linq.Expressions;

class Program{

    const long MOD =1000000007;
   
    static void Main(string[] args)
    {
        int[] num = ScanIntArray(2);
        int n = num[0];
        int d = num[1];
        int ans;
        if(n%(2*d+1) == 0)
        {       
            ans = n / (2 * d + 1);
        }
        else
        {
            ans = n / (2 * d + 1) + 1;
        }

        Console.WriteLine(ans);
    }

 

   static int[] ruiseki(int[] array)
        // Watch Out For OverFlow
    {
        int[] res = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            if (i==0)
            {
                res[i] = array[i];
            }
            else
            {
                res[i] = res[i - 1] + array[i];
            }
        }
        return res;
    }
    static int Nibutan(long[] array, long k)
        // 以上・未満などをちゃんと見ること！
    {
        int low = 0 ;
        int high = array.Length-1;
        int mid = high;

        while (low < high)
        {
            mid = (low + high) / 2;
            if(array[mid] >= k) // k以上の最小index.ココを変えるだけ
            {
                high = mid;
            }
            else
            {
                low = mid + 1;
            }
            mid = (low + high) / 2;
        }
        return mid;
    }

    static int ScanOneInt()
    {
        return int.Parse(Console.ReadLine());
    }

    static long ScanOneLong()
    {
        return long.Parse(Console.ReadLine());
    }

    static string[] ScanStringArray(int lines)
    {
        string[] str = new string[lines];
        for (int i = 0; i < lines; i++)
        {
            str[i] = Console.ReadLine();
        }
        return str;
    }
    static int[] ScanIntArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] ar = new int[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = int.Parse(str[i]);
        }
        return ar;
    }

    static Tuple<int,int> ScanTuple()
    {
        int[] tmp = ScanIntArray(2);
        return new Tuple<int, int>(tmp[0], tmp[1]);
    }
    static long[] ScanLongArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        long[] ar = new long[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = long.Parse(str[i]);
        }
        return ar;
    }

    static string[] ScanStringArray()
    {
        return Console.ReadLine().Split(' ');
    }

    static double[] ScanDoubleArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        double[] ar = new double[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = double.Parse(str[i]);
        }
        return ar;
    }

    static int[,] ScanIntSquareArray(int h, int w)
    {
        int[,] resAr = new int[h, w];
        for (int i = 0; i < h; i++)
        {
            int[] ar = ScanIntArray(w);
            for (int j = 0; j < w; j++)
            {
                resAr[i, j] = ar[j];
            }
        }
        return resAr;
    }


    static int[,] CombModMake()
    {
        int[,] res = new int[2005, 2005];
        for (int i = 0; i < 2005; i++)
        {
            for (int j = 0; j < 2005; j++)
            {
                if (i == 0 || i < j)
                {
                    res[i, j] = 0;
                }
                else if (j == 0 || i == j)
                {
                    res[i, j] = 1;
                }
                else
                {
                    res[i, j] = (res[i - 1, j] + res[i - 1, j - 1]) % (int)MOD;
                }
            }
        }
        return res;
    }

    // int, long両方で出来るGCDを作った
    static T GCD<T>(T a, T b)
    {
        if((dynamic)a % (dynamic)b == 0)
        {
            return b;
        }
        else
        {
            return GCD((dynamic)b, (dynamic)a % (dynamic)b);
        }
    }



}

public class Dijkstra // 書きかけ
{
    private int maxIndex = -1;
    private const long INF = Int64.MaxValue;
}

public class SegmentTree<T>
{
    int dat_size;
    T[] Tree;
    public SegmentTree(T[] dat)
    {
        this.dat_size = dat.Length;

        Init(dat_size);
    }

    // Segment Treeの初期化.
    // dat_sizeを超えるような最小の2のべき乗がsizeになる(末尾は使わない)
    void Init(int dat_size)
    {
        int n = 1;
        while (n < dat_size) n *= 2;
        Tree = new T[n];
    }

    void Bulid(int dat_size, T[] dat, T[] tree)
    {
        for (int i = 0; i < tree.Length; i++)
        {
            tree[i + dat.Length - 1] = dat[i];
        }
        for (int i = tree.Length - 1; i >= 0; i--)
        {
            tree[i] = Func(tree[i * 2], tree[i * 2 + 1]);
        }
    }

    T Func(T o1, T o2)
    {
        T res;
        //
        // 何かしら操作
        res = Math.Min((dynamic)o1, (dynamic)o2);
        //
        return res;
    }
}

public class Pair<T,U>: IComparable where T : IComparable<T> where U: IComparable<U>
{
    public T Item1;
    public U Item2;

    public int  CompareTo(object obj)
    {
        Pair<T,U> pair = (Pair<T, U>)obj;
        return Item1.CompareTo(pair.Item1);
    }
    public Pair(T t, U u)
    {
        Item1 = t;
        Item2 = u;
    }

}



// 平衡二分木
// 計算量: Push -> O(logN), Peek -> O(1)。Clear() -> O(logN)
// ToArray()で配列化
public class PriorityQueue<T> where T : IComparable
{
    private IComparer<T> _comparer = null;
    private int _type = 0;
    private T[] _heap;
    private int _sz = 0;
    private int _count = 0;

    /// <summary>
    /// Priority Queue with custom comparer
    /// </summary>
    public PriorityQueue(int maxSize, IComparer<T> comparer)
    {
        _heap = new T[maxSize];
        _comparer = comparer;
    }

    /*
     -> Item: _heap(ヒープを持つ.sizeはmaxSize)
     -> Item: _type -> 0:asc(昇順), 1:desc(降順)
     */
    public PriorityQueue(int maxSize, int type = 0)
    {
        _heap = new T[maxSize];
        _type = type;
    }

    private int Compare(T x, T y)
    {
        if (_comparer != null) return _comparer.Compare(x, y);
        return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        // typeが0なら昇順, 1なら降順にソートするCompare
    }

    public void Push(T x)
    {
        _count++;

        //node number
        var i = _sz++;

        while (i > 0)
        {
            //parent node number
            var p = (i - 1) / 2;
            if (Compare(_heap[p], x) <= 0) break;
            _heap[i] = _heap[p];
            i = p;
        }

        _heap[i] = x;
    }

    public T Pop()
    {
        _count--;

        T ret = _heap[0];
        T x = _heap[--_sz];

        int i = 0;
        while (i * 2 + 1 < _sz)
        {
            //children
            int a = i * 2 + 1;
            int b = i * 2 + 2;

            if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

            if (Compare(_heap[a], x) >= 0) break;

            _heap[i] = _heap[a];
            i = a;
        }

        _heap[i] = x;

        return ret;
    }

    public int Count()  // O(1)
    {
        return _count;
    }

    public T Peek() // O(1)
    {
        return _heap[0];
    }

    public bool Contains(T x)   // O(N)なので注意
    {
        for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
        return false;
    }

    public void Clear()
    {
        while (Count() > 0) Pop();
    }

    public IEnumerator<T> GetEnumerator() // なにこれ
    {
        var ret = new List<T>();

        while (Count() > 0)
        {
            ret.Add(Pop());
        }

        foreach (var r in ret)
        {
            Push(r);
            yield return r;
        }
    }

    public T[] ToArray()
    {
        T[] array = new T[_sz];
        int i = 0;

        foreach (var r in this)
        {
            array[i++] = r;
        }

        return array;
    }
}



public class GenericOperation<T>
{
    public GenericOperation()
    {
        var availableT = new Type[]
        {
            typeof(int), typeof(uint), typeof(short), typeof(ushort), typeof(long), typeof(ulong), typeof(byte),
            typeof(decimal), typeof(double)
        };
        if (!availableT.Contains(typeof(T)))
        {
            throw new NotSupportedException();
        }
        var p1 = Expression.Parameter(typeof(T));
        var p2 = Expression.Parameter(typeof(T));
        Add = Expression.Lambda<Func<T, T, T>>(Expression.Add(p1, p2), p1, p2).Compile();
        Subtract = Expression.Lambda<Func<T, T, T>>(Expression.Subtract(p1, p2), p1, p2).Compile();
        Multiply = Expression.Lambda<Func<T, T, T>>(Expression.Multiply(p1, p2), p1, p2).Compile();
        Divide = Expression.Lambda<Func<T, T, T>>(Expression.Divide(p1, p2), p1, p2).Compile();
        Modulo = Expression.Lambda<Func<T, T, T>>(Expression.Modulo(p1, p2), p1, p2).Compile();
        Equal = Expression.Lambda<Func<T, T, bool>>(Expression.Equal(p1, p2), p1, p2).Compile();
        GreaterThan = Expression.Lambda<Func<T, T, bool>>(Expression.GreaterThan(p1, p2), p1, p2).Compile();
        GreaterThanOrEqual = Expression.Lambda<Func<T, T, bool>>(Expression.GreaterThanOrEqual(p1, p2), p1, p2).Compile();
        LessThan = Expression.Lambda<Func<T, T, bool>>(Expression.LessThan(p1, p2), p1, p2).Compile();
        LessThanOrEqual = Expression.Lambda<Func<T, T, bool>>(Expression.LessThanOrEqual(p1, p2), p1, p2).Compile();
    }

    public Func<T, T, T> Add { get; private set; }
    public Func<T, T, T> Subtract { get; private set; }
    public Func<T, T, T> Multiply { get; private set; }
    public Func<T, T, T> Divide { get; private set; }
    public Func<T, T, T> Modulo { get; private set; }
    public Func<T, T, bool> Equal { get; private set; }
    public Func<T, T, bool> GreaterThan { get; private set; }
    public Func<T, T, bool> GreaterThanOrEqual { get; private set; }
    public Func<T, T, bool> LessThan { get; private set; }
    public Func<T, T, bool> LessThanOrEqual { get; private set; }
}