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;
using static AtCoderer.Comfort;
using static AtCoderer.Math;
using static AtCoderer.Algorithm;
using static System.Math;

namespace AtCoderer
{
    public class App
    {
        public static void Solve()
        {
            int n,d;
            ParseArray(out n, out d);
            Console.WriteLine((n-1) / (d * 2 + 1)+1);
        }
        public static void Main(string[] args)
        {
            Solve();
            Console.ReadKey();
        }
    }
    public static class Comfort
    {
        public static int[] OrderBy(this int[] IArr)
        {
            int[] arr = new int[IArr.Length];
            Array.Copy(IArr, arr, IArr.Length);
            Array.Sort(arr);
            return arr;
        }
        public static char[] OrderBy(this string IArr)
        {
            char[] arr = new char[IArr.Length];
            Array.Copy(IArr.ToCharArray(), arr, IArr.Length);
            Array.Sort(arr);
            return arr;
        }
        public static int Max(params int[] p) => p.Max();
        public static long Max(params long[] p) => p.Max();
        public static int Min(params int[] p) => p.Min();
        public static long Min(params long[] p) => p.Min();
        public static int Parse()
        {
            return int.Parse(Console.ReadLine());
        }
        public static int[] ParseArray(this string s)
        {
            return s.Split().Select(v => int.Parse(v)).ToArray();
        }
        public static long[] ParseArrayL(this string s)
        {
            return s.Split().Select(v => long.Parse(v)).ToArray();
        }
        public static int[] ParseArray()
        {
            return Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
        }
        public static long[] ParseArrayL()
        {
            return Console.ReadLine().Split().Select(v => long.Parse(v)).ToArray();
        }
        public static void ParseArray(out int a, out int b)
        {
            var r = Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
        }
        public static void ParseArray(out int a, out int b, out int c)
        {
            var r = Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
            c = r[2];
        }
        public static void ParseArray(out int a, out int b, out int c, out int d)
        {
            var r = Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
            c = r[2];
            d = r[3];
        }
        public static void ParseArray(out long a, out long b)
        {
            var r = Console.ReadLine().Split().Select(v => long.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
        }
        public static void ParseArray(out long a, out long b, out long c)
        {
            var r = Console.ReadLine().Split().Select(v => long.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
            c = r[2];
        }
        public static void ParseArray(out long a, out long b, out long c, out long d)
        {
            var r = Console.ReadLine().Split().Select(v => long.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
            c = r[2];
            d = r[3];
        }
        public static string ToString(this IEnumerable<char> v)
        {
            return string.Join("", v);
        }
        public static string Join<T>(this IEnumerable<T> v, char c)
        {
            return string.Join(c.ToString(), v);
        }
        public static string Join<T>(this IEnumerable<T> v, string s)
        {
            return string.Join(s, v);
        }
        public static int[] ReadArr
        {
            get
            {
                return Console.ReadLine().Split().Select(s => int.Parse(s)).ToArray();
            }
        }
    }
    public static class Math
    {
        public static bool IsNatural(this float v) => v - (int)v == 0;
        public static bool IsNatural(this double v) => v - (int)v == 0;
        public static long nCm(long n, long m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * nCm(n - 1, m - 1) / m % 1000000007;
        }
        public static IEnumerable<int> Factor(int n)
        {
            int i = 2;
            int tmp = n;

            while (i * i <= n)
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) yield return tmp;
        }
        public static int Gcd(int a, int b) => a > b ? GcdRecursive(a, b) : GcdRecursive(b, a);
        private static int GcdRecursive(int x, int y) => y == 0 ? x : GcdRecursive(y, x % y);
        public static long Gcd(long a, long b) => a > b ? GcdRecursive(a, b) : GcdRecursive(b, a);
        private static long GcdRecursive(long x, long y) => y == 0 ? x : GcdRecursive(y, x % y);
        public static long Lcm(int a, int b) => ((long)a) * b / Gcd(a, b);
    }
    public static class Algorithm
    {
        public class Point
        {
            public int a;
            public int b;
            public Point(int x, int y)
            {
                a = x;
                b = y;
            }
        }
        public class EnumAll
        {
            bool Over = false;
            int UpperValue;
            int Dimension;
            public int[] Current { private set; get; }
            public EnumAll(int Value, int Dimension)
            {
                this.Dimension = Dimension;
                UpperValue = Value;
                Current = new int[Dimension];
                Current[0] = -1;
            }
            public bool Next()
            {
                if (Over)
                    return false;
                bool flag = false;
                for (int i = 0; i < Dimension; i++)
                {
                    if (++Current[i] >= UpperValue)
                        Current[i] = 0;
                    else
                    {
                        flag = true;
                        break;
                    }
                }
                if (!flag)
                {
                    Over = true;
                    return false;
                }
                return true;
            }
            public bool IsOver()
            {
                return Over;
            }
        }
        public class UnionFind
        {
            private int[] Parent;
            private int GetRoot(int v)
            {
                if (Parent[v] < 0)
                    return v;
                else
                    return Parent[v] = GetRoot(Parent[v]);
            }
            public UnionFind(int size)
            {
                Parent = new int[size];
                for (int i = 0; i < size; i++)
                    Parent[i] = -1;
            }
            public bool AreGrouped(int a, int b)
            {
                return GetRoot(a) == GetRoot(b);
            }
            public void Connect(int a, int b)
            {
                a = GetRoot(a);
                b = GetRoot(b);
                if (a == b) return;
                if (Parent[b] < Parent[a])
                {
                    Parent[b] += Parent[a];
                    Parent[a] = b;
                }
                else
                {
                    Parent[a] += Parent[b];
                    Parent[b] = a;
                }
            }
            public int GetGroupSize(int a)
            {
                return -Parent[GetRoot(a)];
            }
        }
    }
}