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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import java.util.function.*;
// import lib.util.*;
// import lib.graph.*;
// import lib.io.*;
// import lib.math.*;

public class Main {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int N = sc.nextInt();
        int D = sc.nextInt();
        int res = 0;
        while (N > 0) {
            res++;
            N -= 2 * D + 1;
        }

        out.println(res);
        out.flush();
    }
}

class pair {
    int l, r;

    public pair(int l, int r) {
        this.l = l;
        this.r = r;
    }
}

class UnionFindTree {
    int[] root;
    int[] rank;
    int[] size;
    int m;

    public UnionFindTree(int n) {
        this.root = new int[n];
        this.rank = new int[n];
        this.size = new int[n];
        this.m = n;
        for (int i = 0; i < n; i++) {
            root[i] = i;
            size[i] = 1;
        }
    }

    public int find(int x) {
        if (root[x] == x)
            return x;
        else {
            return root[x] = find(root[x]);
        }
    }

    public void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y)
            return;
        if (rank[x] < rank[y]) {
            size[find(y)] = size[find(x)];
            root[x] = y;
        } else {
            size[find(x)] = size[find(y)];
            root[y] = x;
            if (rank[x] == rank[y])
                rank[x]++;
        }
        m--;
    }

    public boolean same(int x, int y) {
        return find(x) == find(y);
    }

    public int size(int i) {
        return this.size[find(i)];
    }
}

class Dijkstra {
    private static int prev[];
    private static long dist[];

    public Dijkstra(AbstractGraph graph, int s) {
        prev = new int[graph.n];
        dist = new long[graph.n];
        Arrays.fill(prev, -1);
        Arrays.fill(dist, Long.MAX_VALUE);
        PriorityQueue<Integer> searching = new PriorityQueue<>((x, y) -> Long.compare(dist[x], dist[y]));
        dist[s] = 0;
        searching.add(s);
        while (searching.size() > 0) {
            int now = searching.poll();
            for (Edge e : graph.getEdges(now)) {
                int next = e.to;
                long c = e.cost;
                if (dist[now] + c < dist[next]) {
                    dist[next] = dist[now] + c;
                    prev[next] = now;
                    searching.add(next);
                }
            }
        }
    }

    public int[] path(int to) {
        ArrayList<Integer> rev = new ArrayList<>();
        for (int now = to; now != -1; now = this.prev[now]) {
            rev.add(now);
        }
        int[] path = new int[rev.size()];
        for (int i = 0; i < path.length; i++) {
            path[i] = rev.get(path.length - i - 1);
        }
        return path;
    }
}

class WF {
    private static long[][] dist;

    public WF(AbstractGraph graph) {
        dist = new long[graph.n][graph.n];
        for (int i = 0; i < dist.length; i++) {
            Arrays.fill(dist[i], Integer.MAX_VALUE);
        }
        for (int i = 0; i < graph.n; i++) {
            for (Edge e : graph.getEdges(i)) {
                dist[i][e.to] = e.cost;
            }
            dist[i][i] = 0;
        }
        for (int k = 0; k < graph.n; k++) {
            for (int i = 0; i < graph.n; i++) {
                for (int j = 0; j < graph.n; j++) {
                    if (dist[i][k] != Integer.MAX_VALUE && dist[k][j] != Integer.MAX_VALUE) {
                        dist[i][j] = Math.min(dist[i][j], dist[i][k] + dist[k][j]);
                    }
                }
            }
        }
    }

    public static long getShortest(int s, int t) {
        return dist[s][t];
    }

    public static long[][] getAllDist() {
        return dist;
    }

    public static boolean isNegativeLoop() {
        for (int i = 0; i < dist.length; i++) {
            if (dist[i][i] < 0) {
                return true;
            }
        }
        return false;
    }
}

class Edge {
    int from, to;
    long cost;

    public Edge(int from, int to, long cost) {
        this.from = from;
        this.to = to;
        this.cost = cost;
    }

    public Edge(int from, int to) {
        this.from = from;
        this.to = to;
        this.cost = 1;
    }

    public Edge reverse() {
        return new Edge(to, from, cost);
    }
}

@SuppressWarnings("unchecked")
abstract class AbstractGraph {
    int n;
    int m;
    ArrayList<Edge>[] edges;

    public AbstractGraph(int n) {
        this.n = n;
        this.m = 0;
        this.edges = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            this.edges[i] = new ArrayList<Edge>();
        }
    }

    public void addEdge(Edge e) {
        this.m++;
        this.edges[e.from].add(e);
    }

    public int getV() {
        return this.n;
    }

    public int getE() {
        return this.m;
    }

    public ArrayList<Edge> getEdges(int v) {
        return this.edges[v];
    }

    abstract public boolean isBipartite();

    public boolean isTree() {
        // require Modifying.
        return false;
    }
}

class Graph extends AbstractGraph {
    int n;
    int m;
    // array of edges which is connect to the node
    ArrayList<Edge>[] edges;

    public Graph(int n) {
        super(n);
    }

    public void addEdge(int from, int to, int cost) {
        Edge e = new Edge(from, to, cost);
        super.addEdge(e);
        super.addEdge(e.reverse());
        this.m++;
    }

    @Override
    public void addEdge(Edge e) {
        this.edges[e.from].add(e);
        this.edges[e.to].add(e.reverse());
        this.m++;
    }

    public int getV(int v) {
        return n;
    }

    public int getE() {
        return m;
    }

    public boolean isBipartite() {
        int[] color = new int[n];
        PriorityQueue<Integer> queue = new PriorityQueue<>();
        HashSet<Integer> visited = new HashSet<>();
        queue.add(0);
        color[0] = 1;
        while (queue.size() > 0) {
            int now = queue.poll();
            visited.add(now);
            for (Edge e : getEdges(now)) {
                if (visited.contains(e.to)) {
                    continue;
                }
                if (color[e.to] == color[now])
                    return false;
                queue.add(e.to);
                if (color[e.to] == 0)
                    color[e.to] = -1 * color[now];
            }
        }
        return true;
    }
}

class DirectedGraph extends AbstractGraph {
    int n;
    int m;
    // array of edges which is connect to the node
    ArrayList<Edge>[] edges;

    public DirectedGraph(int n) {
        super(n);
    }

    public void addEdge(int from, int to, int cost) {
        Edge e = new Edge(from, to, cost);
        super.addEdge(e);
        this.m++;
    }

    @Override
    public void addEdge(Edge e) {
        this.edges[e.from].add(e);
        this.m++;
    }

    public int getV(int v) {
        return this.n;
    }

    public int getE() {
        return this.m;
    }

    public boolean isBipartite() {
        // need to rewrite to work
        return false;
    }

}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}

class MyMath {
    public static long gcm(long a, long b) {

        if (a < b)
            return gcm(b, a);

        if (a % b == 0 || b == 0)
            return b;

        long remainder = a % b;
        return gcm(b, remainder);
    }

    public static long summation(long a, long b) {
        return b * (b + 1) / 2 - a * (a - 1) / 2;
    }

    public static long factorial(long n) {

        if (n <= 1)
            return 1;
        else
            return factorial(n - 1) * n;
    }

    public static long[][] binomialTable(int a, long m) {
        long[][] table = new long[a + 1][a + 1];
        for (int i = 0; i < a + 1; i++) {
            table[0][a] = 0;
            table[i][0] = 1;
            table[i][i] = 1;
        }
        for (int i = 1; i < a + 1; i++) {
            for (int j = 1; j < a + 1; j++) {
                if (i < j)
                    table[i][j] = 0;
                else {
                    table[i][j] = (table[i - 1][j - 1] + table[i - 1][j]) % m;
                }
            }
        }
        return table;
    }

    public static long binomial(int n, int k, long m) {
        long res = 1;
        for (int l = n - k + 1; l <= n; l++) {
            res = (res % m) * (l % m) % m;
        }
        for (int r = 1; r <= k; r++) {
            res = (res % m) * modinv(r, m) % m;
        }
        return res;
    }

    public static long repeatSquarePow(long a, long n, long p) {
        if (n == 0)
            return 1;
        if (n == 1)
            return a % p;
        if (n % 2 == 1)
            return a * repeatSquarePow(a, n - 1, p) % p;
        long tmp = repeatSquarePow(a, n / 2, p) % p;
        return tmp * tmp % p;
    }

    public static long modinv(long a, long p) {
        long b, x, u, q, abs_p, tmp;
        abs_p = Math.abs(p);
        b = p;
        x = 1;
        u = 0;
        while (b > 0) {
            q = a / b;
            tmp = u;
            u = x - q * u;
            x = tmp;
            tmp = b;
            b = a - q * b;
            a = tmp;
        }
        return (x < 0) ? abs_p + x : x;
    }

    public static Long[] eratosthenes(int n) {
        Long[] factor_table = new Long[n];
        for (long i = 1; i <= n; i++) {
            factor_table[(int) (i - 1)] = i;
        }
        for (long i = 1; i <= n; i++) {
            if (factor_table[(int) (i - 1)] == i) {
                int j = 2;
                while (i * j <= n) {
                    factor_table[(int) (i * j - 1)] = i;
                    j++;
                }
            }
        }

        return factor_table;
    }

    public static HashMap<Long, Integer> primeFactorization(long n) {
        HashMap<Long, Integer> primes = new HashMap<>();
        for (long p = 2; p * p <= n; p++) {
            int q = 0;
            while (n % p == 0) {
                n /= p;
                q++;
            }
            if (q > 0)
                primes.put(p, q);
        }
        if (n > 1)
            primes.put(n, 1);
        return primes;
    }

    public static ArrayList<Integer> divisor(int n) {
        ArrayList<Integer> ret = new ArrayList<Integer>();
        for (int i = 1; i * i <= n; i++) {
            if (n % i == 0) {
                ret.add(i);
                // n=PQ+0→ PもQも約数. ただし、Q=Pは↑で登録済みなので登録しない
                if (i != n / i)
                    ret.add(n / i);
            }
        }
        return ret;
    }
}

class nextPermutation {
    public static int[] swap(int data[], int left, int right) {

        // Swap the data
        int temp = data[left];
        data[left] = data[right];
        data[right] = temp;

        // Return the updated array
        return data;
    }

    // Function to reverse the sub-array
    // starting from left to the right
    // both inclusive
    public static int[] reverse(int data[], int left, int right) {

        // Reverse the sub-array
        while (left < right) {
            int temp = data[left];
            data[left++] = data[right];
            data[right--] = temp;
        }

        // Return the updated array
        return data;
    }

    // Function to find the next permutation
    // of the given integer array
    public static boolean findNextPermutation(int data[]) {

        // If the given dataset is empty
        // or contains only one element
        // next_permutation is not possible
        if (data.length <= 1)
            return false;

        int last = data.length - 2;

        // find the longest non-increasing suffix
        // and find the pivot
        while (last >= 0) {
            if (data[last] < data[last + 1]) {
                break;
            }
            last--;
        }

        // If there is no increasing pair
        // there is no higher order permutation
        if (last < 0)
            return false;

        int nextGreater = data.length - 1;

        // Find the rightmost successor to the pivot
        for (int i = data.length - 1; i > last; i--) {
            if (data[i] > data[last]) {
                nextGreater = i;
                break;
            }
        }

        // Swap the successor and the pivot
        data = swap(data, nextGreater, last);

        // Reverse the suffix
        data = reverse(data, last + 1, data.length - 1);

        // Return true as the next_permutation is done
        return true;
    }
}

class ArrayUtil {
    private static long INF = 1_000_000_000_0L;

    public static int UpperBound(long[] array, long obj) {
        int l = 0, r = array.length - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj < array[c]) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }

    public static int LowerBound(long[] array, long obj) {
        int l = 0, r = array.length - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj <= array[c]) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }

    // return the length of array's LIS
    public static int LIS(long[] array) {
        long[] dp = new long[array.length + 1];
        Arrays.fill(dp, INF);
        for (int i = 0; i < array.length; i++) {
            int idx = LowerBound(dp, array[i]);
            dp[idx] = array[i];
        }
        return LowerBound(dp, INF - 1);
    }

    public static int StrictLIS(long[] array) {
        long[] dp = new long[array.length + 1];
        Arrays.fill(dp, INF);
        for (int i = 0; i < array.length; i++) {
            int idx = UpperBound(dp, array[i]);
            dp[idx] = array[i];
        }
        return UpperBound(dp, INF - 1);
    }
}