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.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC134.B();
        }
        class ABC134
        {
            public static void A()
            {
                var R = Read.Int();
                Console.WriteLine(3 * R * R);
            }
            public static void B()
            {
                var N = Read.Int();
                var D = Read.Int();
                Console.WriteLine((N + D * 2) / (D * 2 + 1));
            }
            public static void C()
            {
                var N = Read.Int();
                var A = Enumerable.Range(0, N).Select(i => Read.Long()).ToArray();
                var AS = A.OrderBy(x => -x).ToArray();
                var sb = new System.Text.StringBuilder();
                for(int i = 0; i < N; ++i)
                {
                    sb.AppendLine((A[i] == AS[0] ? AS[1] : AS[0]).ToString());
                }
                Console.Write(sb.ToString());
            }
            public static void D()
            {
                var N = Read.Int();
                var A = Read.IntN();
                var ans = new int[N + 1];
                for(int i = N; i > 0; --i)
                {
                    int sum = 0;
                    for(int m=2; ; ++m)
                    {
                        if (i * m > N) { break; }
                        sum += ans[i * m];
                    }
                    ans[i] = (A[i - 1] + sum) % 2;
                }
                var ans1 = Enumerable.Range(1, N).Where(i => ans[i] > 0).ToArray();
                Console.WriteLine(ans1.Length);
                if (ans1.Length > 0)
                {
                    Console.WriteLine(String.Join(" ", ans1));
                }
            }
            public static void E()
            {
                var N = Read.Int();
                var A = Enumerable.Range(0, N).Select(i => Read.Int()).ToArray();
                var set = new Util.MultiSet<int>();
                for(int i = 0; i < N; ++i)
                {
                    var idx = set.LowerBound(A[i]);
                    if (idx > 0)
                    {
                        set.Remove(set.ElementAt(idx - 1));
                    }
                    set.Insert(A[i]);
                }
                Console.WriteLine(set.Count());
            }
            public static void F()
            {

            }
        }



        class Util
        {
            public class BST<T> where T : IComparable
            {
                public class Node
                {
                    public T V;
                    public Node L, R;
                    public int Count;
                    public Node(T v) { V = v; Count = 1; }
                }
                static Random _rnd = new Random();
                public static int Count(Node t) { return t == null ? 0 : t.Count; }
                static Node Update(Node t) { t.Count = Count(t.L) + Count(t.R) + 1; return t; }
                public static Node Merge(Node l, Node r)
                {
                    if (l == null || r == null) return l == null ? r : l;
                    if ((double)Count(l) / (double)(Count(l) + Count(r)) > _rnd.NextDouble())
                    { l.R = Merge(l.R, r); return Update(l); }
                    else { r.L = Merge(l, r.L); return Update(r); }
                }
                public static Tuple<Node, Node> Split(Node t, int k)
                {
                    if (t == null) return new Tuple<Node, Node>(null, null);
                    if (k <= Count(t.L))
                    {
                        var s = Split(t.L, k);
                        t.L = s.Item2;
                        return new Tuple<Node, Node>(s.Item1, Update(t));
                    }
                    else
                    {
                        var s = Split(t.R, k - Count(t.L) - 1);
                        t.R = s.Item1;
                        return new Tuple<Node, Node>(Update(t), s.Item2);
                    }
                }
                public static Node Remove(Node t, T v)
                {
                    if (Find(t, v) == null) return t;
                    return RemoveAt(t, LowerBound(t, v));
                }
                public static Node RemoveAt(Node t, int k)
                {
                    var s = Split(t, k);
                    var s2 = Split(s.Item2, 1);
                    return Merge(s.Item1, s2.Item2);
                }
                public static bool Contains(Node t, T v) { return Find(t, v) != null; }
                public static Node Find(Node t, T v)
                {
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);
                        if (cmp > 0) t = t.L;
                        else if (cmp < 0) t = t.R;
                        else break;
                    }
                    return t;
                }

                public static Node FindByIndex(Node t, int idx)
                {
                    if (t == null) return null;
                    var currentIdx = Count(t) - Count(t.R) - 1;
                    while (t != null)
                    {
                        if (currentIdx == idx) return t;
                        if (currentIdx > idx)
                        { t = t.L; currentIdx -= (Count(t == null ? null : t.R) + 1); }
                        else { t = t.R; currentIdx += (Count(t == null ? null : t.L) + 1); }
                    }
                    return null;
                }
                public static int UpperBound(Node t, T v)
                {
                    var torg = t;
                    if (t == null) return -1;

                    var ret = Int32.MaxValue;
                    var idx = Count(t) - Count(t.R) - 1;
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);

                        if (cmp > 0)
                        {
                            ret = Math.Min(ret, idx);
                            t = t.L;
                            idx -= (Count(t == null ? null : t.R) + 1);
                        }
                        else if (cmp <= 0)
                        {
                            t = t.R;
                            idx += (Count(t == null ? null : t.L) + 1);
                        }
                    }
                    return ret == Int32.MaxValue ? Count(torg) : ret;
                }
                public static int LowerBound(Node t, T v)
                {
                    var torg = t;
                    if (t == null) return -1;

                    var idx = Count(t) - Count(t.R) - 1;
                    var ret = Int32.MaxValue;
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);
                        if (cmp >= 0)
                        {
                            if (cmp == 0) ret = Math.Min(ret, idx);
                            t = t.L;
                            if (t == null) ret = Math.Min(ret, idx);
                            idx -= t == null ? 0 : (Count(t.R) + 1);
                        }
                        else if (cmp < 0)
                        {
                            t = t.R;
                            idx += (Count(t == null ? null : t.L) + 1);
                            if (t == null) return idx;
                        }
                    }
                    return ret == Int32.MaxValue ? Count(torg) : ret;
                }
                public static Node Insert(Node t, T v)
                {
                    var ub = LowerBound(t, v);
                    return InsertByIdx(t, ub, v);
                }
                static Node InsertByIdx(Node t, int k, T v)
                {
                    var s = Split(t, k);
                    return Merge(Merge(s.Item1, new Node(v)), s.Item2);
                }
                public static IEnumerable<T> Enumerate(Node t)
                {
                    var ret = new List<T>();
                    Enumerate(t, ret);
                    return ret;
                }
                static void Enumerate(Node t, List<T> ret)
                {
                    if (t == null) return;
                    Enumerate(t.L, ret);
                    ret.Add(t.V);
                    Enumerate(t.R, ret);
                }
            }
            public class Set<T> where T : IComparable
            {
                protected BST<T>.Node _root;
                public T this[int idx] { get { return ElementAt(idx); } }
                public int Count() { return BST<T>.Count(_root); }
                public virtual void Insert(T v)
                {
                    if (_root == null) _root = new BST<T>.Node(v);
                    else
                    {
                        if (BST<T>.Find(_root, v) != null) return;
                        _root = BST<T>.Insert(_root, v);
                    }
                }
                public void Clear() { _root = null; }
                public void Remove(T v) { _root = BST<T>.Remove(_root, v); }
                public bool Contains(T v) { return BST<T>.Contains(_root, v); }
                public T ElementAt(int k)
                {
                    var node = BST<T>.FindByIndex(_root, k);
                    if (node == null) throw new IndexOutOfRangeException();
                    return node.V;
                }
                public int Count(T v) { return BST<T>.UpperBound(_root, v) - BST<T>.LowerBound(_root, v); }
                public int LowerBound(T v) { return BST<T>.LowerBound(_root, v); }
                public int UpperBound(T v) { return BST<T>.UpperBound(_root, v); }
                public Tuple<int, int> EqualRange(T v)
                {
                    if (!Contains(v)) return new Tuple<int, int>(-1, -1);
                    return new Tuple<int, int>(BST<T>.LowerBound(_root, v), BST<T>.UpperBound(_root, v) - 1);
                }
                public List<T> ToList() { return new List<T>(BST<T>.Enumerate(_root)); }
            }
            public class MultiSet<T> : Set<T> where T : IComparable { public override void Insert(T v) { if (_root == null) { _root = new BST<T>.Node(v); } else { _root = BST<T>.Insert(_root, v); } } }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}