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.IO;
using System.Linq;
using System.Reflection;
using System.Text;

namespace A
{
    partial class Program
    {
        public IEnumerable<string> Solve()
        {
            var n = Scan;
            var d = Scan;
            var res = (n - 1) / (d * 2 + 1) + 1;
            yield return res.ToString();
        }
    }

    class StartingPoint
    {
        static void Main(string[] args)
        {
            if (args?.Any() == true)
            {
                var assembly = Assembly.GetEntryAssembly();
                var resourceName = "AtCoderCSharp.In.txt";
                var stream = assembly.GetManifestResourceStream(resourceName);
                var streamReader = new StreamReader(stream, Encoding.UTF8);
                var str = streamReader.ReadToEnd();
                var textReader = new StringReader(str);
                Console.SetIn(textReader);
            }

            try
            {
                foreach (var s in new Program().Solve())
                {
                    Console.WriteLine(s);
                }
            }
            catch (Exception e)
            {
                Console.WriteLine(e);
                if (args?.Any() != true)
                    throw e;
            }

            if (args?.Any() == true)
                Console.ReadKey();
        }
    }

    partial class Program
    {
        public List<int> ScanInts(int count) => Enumerable.Range(0, count).Select(_ => ScanInt).ToList();
        public List<int> ScanInts(long count) => ScanInts((int)count);
        public List<long> ScanLongs(int count) => Enumerable.Range(0, count).Select(_ => Scan).ToList();
        public List<long> ScanLongs(long count) => ScanLongs((int)count);
        public int ScanInt => int.Parse(Str);
        public long Scan => long.Parse(Str);
        public double ScanDouble => (double)Scan;

        StringBuilder sb = new StringBuilder();

        public string Str => ScanStr();
        public string ScanStr()
        {
            sb.Clear();

            int r = 0;
            bool? b = null;
            do
            {
                r = Console.Read();
                b = IsBreak(r);
            } while (b == true);

            if (b == null)
                throw new Exception("input error: unexpected end of stream");

            do
            {
                sb.Append((char)r);
                r = Console.Read();
                b = IsBreak(r);
            } while (b == false);

            return sb.ToString();
        }

        bool? IsBreak(int c)
        {
            switch (c)
            {
                case -1:
                    return null;
                case (int)' ':
                case (int)'\n':
                case (int)'\r':
                    return true;
                default:
                    return false;
            }
        }

        public IEnumerable<int> Loop(int count) => Enumerable.Range(0, count);
        public IEnumerable<int> Loop(int from, int to) => Enumerable.Range(from, to - from + 1);

        public string YesNo(bool isYes) => isYes ? "Yes" : "No";

        public HashSet<T> ToHashSet<T>(IEnumerable<T> ts) => new HashSet<T>(ts);

        public int Gcm(int a, int b)
        {
            if (a < b)
                return GcmImpl(b, a);
            else
                return GcmImpl(a, b);
        }

        int GcmImpl(int a, int b)
        {
            var remainder = a % b;
            if (remainder == 0)
                return b;
            else
                return GcmImpl(b, remainder);
        }

        public int Lcm(int a, int b)
        {
            return a / Gcm(a, b) * b;
        }
    }

    class Mod
    {
        readonly int _divider = 1000000007;
        public Mod(int divider = 1000000007)
        {
            _divider = divider;
        }

        public int Add(int a, int b) => (int)Add((long)a, (long)b);
        public int Sub(int a, int b) => (int)Sub((long)a, (long)b);
        public int Mul(int a, int b) => (int)Mul((long)a, (long)b);
        public int Div(int a, int b) => (int)Div((long)a, (long)b);
        public int Pow(int a, int p) => (int)Pow((long)a, (long)p);

        public long Add(long a, long b) => (a + b) % _divider;

        public long Sub(long a, long b)
        {
            var t = (a - b) % _divider;
            if (t < 0)
                t += _divider;
            return t;
        }

        public long Mul(long a, long b) => (a * b) % _divider;

        public long Div(long a, long b) => Mul(a, Inv(b));

        public long Pow(long a, long p)
        {
            switch (p)
            {
                case 0: return 1;
                case 1: return a;
                default:
                    var halfP = p / 2;
                    var halfPowered = Pow(a, halfP);
                    var powered = Mul(halfPowered, halfPowered);
                    return p % 2 == 0 ? powered : Mul(powered, a);
            }
        }

        readonly Dictionary<long, long> invCache = new Dictionary<long, long>();
        long Inv(long a)
        {
            long cache = 0L;
            if (invCache.TryGetValue(a, out cache))
                return cache;

            var result = Pow(a, _divider - 2);
            invCache.Add(a, result);
            return result;
        }

        readonly List<int> facCache = new List<int>() { 1 };
        public int Fac(int a)
        {
            if (a < facCache.Count)
                return facCache[a];

            var val = facCache.Last();
            var start = facCache.Count;
            for (int i = start; i <= a; i++)
            {
                val = Mul(val, i);
                facCache.Add(val);
            }

            return val;
        }

        public int Perm(int n, int r)
        {
            if (n < r)
                return 0;

            if (r <= 0)
                return 1;

            int nn = Fac(n);
            int nr = Fac(n - r);
            return Div(nn, nr);
        }

        public int Comb(int n, int r)
        {
            if (n < r)
                return 0;

            if (n == r)
                return 1;

            int nn = Fac(n);
            int nr = Fac(n - r);
            int rr = Fac(r);
            return Div(Div(nn, nr), rr);
        }
    }
}