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)

namespace AtCoder
{
    using System;
    using System.Collections.Generic;
    using System.IO;
    using System.Linq;
    using System.Text;
    using static System.Console;
    using static System.Math;
    using static Util;

    class AtCoder
    {
        /*------------------------------------------------------------------*/
        private int N, D;
        void Solve()
        {
            io.i(out N,out D);
            var cover = D * 2 + 1;
            if (N % cover == 0)
            {
                (N/cover).Prt();
            }
            else
            {
                (N/cover+1).Prt();
            }
        }

        /*------------------------------------------------------------------*/
        void Test()
        {
            //--- TEST ---//
        }

        public static void Main(string[] _) => new AtCoder().Stream();
        IO io = new IO();

        private void Stream()
        {
            /*
            var exStdIn = new System.IO.StreamReader("stdin.txt");
            SetIn(exStdIn);
            Test();
            */
            Solve();
            io.Flush();
        }
    }

    class IO
    {
        #region INPUT

        #region FastRead

        private const int Size = 1 << 12;
        private readonly Stream _stream = OpenStandardInput();
        private readonly byte[] _buffer = new byte[Size];
        private int _ptr = 0, _buffLen = 0;

        private bool HasNextByte()
        {
            if (_ptr < _buffLen) return true;
            _ptr = 0;
            _buffLen = _stream.Read(_buffer, 0, Size);
            return _buffLen > 0;
        }

        private byte ReadByte()
        {
            if (HasNextByte()) return _buffer[_ptr++];
            else
                //inputの末尾の改行がないとerror
                throw new EndOfStreamException();
        }

        private bool IsAscii(int c) => '!' <= c && c <= '~';

        private char NextChar()
        {
            var b = ReadByte();
            while (!IsAscii(b)) b = ReadByte();
            return (char) b;
        }

        private string Next()
        {
            var sb = new StringBuilder();
            for (var b = NextChar(); IsAscii(b); b = (char) ReadByte()) sb.Append(b);
            return sb.ToString();
        }

        public string String => Next();
        public char Char => NextChar();
        public int Int => int.Parse(Next());
        public long Long => long.Parse(Next());
        public double Double => double.Parse(Next());

        #endregion

        #region LazyRead

        private void scan<T>(ref T x)
        {
            if (x is int) __refvalue(__makeref(x), int) = int.Parse(Next());
            else if (x is long) __refvalue(__makeref(x), long) = long.Parse(Next());
            else if (x is double) __refvalue(__makeref(x), double) = double.Parse(Next());
            else if (x is char) __refvalue(__makeref(x), char) = NextChar();
            else __refvalue(__makeref(x), string) = Next();
        }

        public void i<T>(out T t)
        {
            t = default(T);
            scan(ref t);
        }

        public void i<T, TU>(out T t, out TU u)
        {
            i(out t);
            i(out u);
        }

        public void i<T, TU, TV>(out T t, out TU u, out TV v)
        {
            i(out t, out u);
            i(out v);
        }

        public void i<T, TU, TV, TW>(out T t, out TU u, out TV v, out TW w)
        {
            i(out t, out u);
            i(out v, out w);
        }

        public void i<T, TU, TV, TW, TX>(out T t, out TU u, out TV v, out TW w, out TX x)
        {
            i(out t, out u, out v);
            i(out w, out x);
        }

        public void i<T, TU, TV, TW, TX, TY>(out T t, out TU u, out TV v, out TW w, out TX x, out TY y)
        {
            i(out t, out u, out v);
            i(out w, out x, out y);
        }

        public void ini<T>(out T[] a, int n)
        {
            a = new T[n];
            for (int i = 0; i < n; ++i) i<T>(out a[i]);
        }

        public void ini<T, TU>(out T[] a, out TU[] b, int n)
        {
            a = new T[n];
            b = new TU[n];
            for (int i = 0; i < n; ++i) i<T, TU>(out a[i], out b[i]);
        }

        public void ini<T, TU, TV>(out T[] a, out TU[] b, out TV[] c, int n)
        {
            a = new T[n];
            b = new TU[n];
            c = new TV[n];
            for (var i = 0; i < n; ++i) i<T, TU, TV>(out a[i], out b[i], out c[i]);
        }

        public void ini<T>(out T[,] a, int h, int w)
        {
            a = new T[h, w];
            for (int i = 0; i < h; ++i)
            for (int j = 0; j < w; ++j)
                i<T>(out a[i, j]);
        }

        #endregion

        #endregion

        #region OUTPUT

        private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput())
        {
#if DEBUG
            AutoFlush = true
#else
        AutoFlush = false
#endif
        };

        public void Flush() => Out.Flush();
        public void YN(bool f) => yn(f, "YES", "NO");
        public void Yn(bool f) => yn(f, "Yes", "No");
        public void yn(bool f, string y = "yes", string n = "no") => WriteLine(f ? y : n);

        #endregion

        public IO()
        {
            SetOut(_sw);
        }
    }

    static class Util
    {
        public static T Id<T>(T x) => x;
        public static void FOR(int a, int b, Action<int> f) => FOR(a, b, 1, f);

        public static void FOR(int a, int b, int n, Action<int> f)
        {
            for (int i = a; i < b; i += n) f(i);
        }

        public static void FOREQ(int a, int b, int n, Action<int> f) => FOR(a, b + 1, n, f);
        public static void FOREQ(int a, int b, Action<int> f) => FOR(a, b + 1, f);
        public static void REP(int a, Action<int> f) => FOR(0, a, f);
        public static void REPEQ(int a, Action<int> f) => FOR(0, a + 1, f);

        public static IEnumerable<TResult> ZIP<T1, T2, TResult>(IEnumerable<T1> xs, IEnumerable<T2> ys,
            Func<T1, T2, TResult> f = null)
        {
            using (var e1 = xs.GetEnumerator())
            using (var e2 = ys.GetEnumerator())
                while (e1.MoveNext() && e2.MoveNext())
                    yield return f(e1.Current, e2.Current);
        }

        public static IEnumerable<Tuple<T1, T2>> ZIP<T1, T2>(IEnumerable<T1> xs, IEnumerable<T2> ys)
            => ZIP(xs, ys, (x, y) => new Tuple<T1, T2>(x, y));

        public static IEnumerable<TResult> ZIP<T1, T2, T3, TResult>(IEnumerable<T1> xs, IEnumerable<T2> ys,
            IEnumerable<T3> zs, Func<T1, T2, T3, TResult> f)
        {
            using (var e1 = xs.GetEnumerator())
            using (var e2 = ys.GetEnumerator())
            using (var e3 = zs.GetEnumerator())
                while (e1.MoveNext() && e2.MoveNext() && e3.MoveNext())
                    yield return f(e1.Current, e2.Current, e3.Current);
        }

        public static IEnumerable<Tuple<T1, T2, T3>> ZIP<T1, T2, T3>(IEnumerable<T1> xs, IEnumerable<T2> ys,
            IEnumerable<T3> zs) => ZIP(xs, ys, zs, (x, y, z) => new Tuple<T1, T2, T3>(x, y, z));

        public static bool ODD(int x) => x % 2 != 0;
        public static bool ODD(long x) => x % 2L != 0L;
        public static bool EVE(int x) => !ODD(x);
        public static bool EVE(long x) => !ODD(x);
        public static T MAX<T>(params T[] xs) => xs.Max();
        public static T MIN<T>(params T[] xs) => xs.Min();
        public static int SUM(params int[] xs) => xs.Sum();
        public static long SUM(params long[] xs) => xs.Sum();

        public static IEnumerable<int> RANGE(int start, int step = 1)
        {
            var v = start;
            while (true)
            {
                yield return v;
                v += step;
            }
        }

        public struct IndexedItem<T>
        {
            public int Idx;
            public T Val;

            public IndexedItem(int idx, T val)
            {
                Idx = idx;
                Val = val;
            }
        }

        public class Counts<T> : Dictionary<T, int>
        {
            public Counts()
            {
            }

            public Counts(params T[] xs) : this()
            {
                Add(xs);
            }

            public Counts(IEnumerable<T> xs) : this()
            {
                foreach (var x in xs) Add(x);
            }

            public new int this[T key]
            {
                get
                {
                    int v;
                    return this.TryGetValue(key, out v) ? v : 0;
                }
            }

            public void Add(T key)
            {
                if (!base.ContainsKey(key)) base.Add(key, 0);
                base[key]++;
            }

            public void Add(params T[] xs) => xs.Iter(Add);

            public IEnumerable<KeyValuePair<T, int>> SortByCount(bool isAsc) =>
                (isAsc ? (this.OrderBy(kp => kp.Value)) : (this.OrderByDescending(kp => kp.Value)))
                .ThenBy(kp => kp.Key);
        }

        public class PriorityQueue<T> where T : IComparable<T>
        {
            private List<T> heap;
            private readonly bool isAsc;
            private int size;
            public T Peek => heap[0];
            public int Count => size;
            public bool Any => size > 0;
            public bool Empty => !Any;

            public IEnumerable<T> Values => heap;

            public PriorityQueue(bool isAsc = true)
            {
                this.isAsc = isAsc;
                size = 0;
                heap = new List<T>();
            }

            public void Enqueue(T item)
            {
                heap.Add(item);
                var i = size++;
                while (i > 0)
                {
                    var p = (i - 1) / 2;
                    if (Compare(heap[p], item) <= 0) break;
                    heap[i] = heap[p];
                    i = p;
                }

                heap[i] = item;
            }

            public T Dequeue()
            {
                var ret = heap[0];
                var x = heap[--size];
                var i = 0;
                while ((i << 1) + 1 < size)
                {
                    var a = (i << 1) + 1;
                    var b = (i << 1) + 2;
                    if (b < size && Compare(heap[b], heap[a]) < 0) a = b;
                    if (Compare(heap[a], x) >= 0) break;
                    heap[i] = heap[a];
                    i = a;
                }

                heap[i] = x;
                heap.RemoveAt(size);
                return ret;
            }

            private int Compare(T x, T y) => isAsc ? x.CompareTo(y) : y.CompareTo(x);
        }
    }

    static class Ex
    {
        public static Tuple<IEnumerable<T>, IEnumerable<T>> Split<T>(this IEnumerable<T> xs, Func<T, bool> f)
        {
            var ys = xs.Where(f);
            var zs = xs.Where(x => !f(x));
            return Tuple.Create(ys, zs);
        }

        public static void Iter<T>(this IEnumerable<T> xs, Action<T> f)
        {
            foreach (var x in xs) f(x);
        }

        public static void Prt<T>(this T x) => WriteLine(x);
        public static void Prt<T>(this IEnumerable<T> xs) => xs.Iter(x => WriteLine(x));

        public static void Log<T>(this T x)
        {
#if DEBUG
            WriteLine($"LOG [{nameof(x)}] : {x}");
#endif
        }

        public static IEnumerable<IndexedItem<T>> Indexed<T>(this IEnumerable<T> xs) =>
            xs.Select((x, idx) => new IndexedItem<T>(idx, x));

        public static IEnumerable<T> UnIndexed<T>(this IEnumerable<IndexedItem<T>> xs) => xs.Select(x => x.Val);

        public static IEnumerable<Tuple<T, T>> Pairwise<T>(this IEnumerable<T> xs) => ZIP(xs, xs.Skip(1));

        public static IEnumerable<int> ToZeroIndexed(this IEnumerable<int> xs) => xs.Select(x => x - 1);

        public static string Join<T>(this IEnumerable<T> xs, string str = " ") => String.Join(str, xs);

        public static string Sort(this string s)
        {
            var arr = s.ToCharArray();
            Array.Sort(arr);
            return new string(arr);
        }

        public static string Yn(this bool f, string y = "Yes", string n = "No") => f ? y : n;
        public static bool Is<T>(this T x, Func<T, bool> f) => f(x);
        public static TU Fun<T, TU>(this T x, Func<T, TU> f) => f(x);
    }
}