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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>

int main(void) {
  int N = 0; // 木の本数
  int D = 0; // 配置された木から監視できる範囲
  int monitoring_range = 0; // 監視員が監視できる最大本数
  int watchmans = 0; // 監視員の最低必要人数

  // 木の本数を設定する
  scanf("%d", &N);

  // 監視範囲を設定する
  scanf("%d", &D);

  // 監視員の監視本数を求める
  monitoring_range = D * 2 + 1;

  // 監視範囲の合計から監視員の最低必要人数を求める
  watchmans = N / monitoring_range;
  if(N % monitoring_range) watchmans += 1;

  // 監視員の最低必要人数を出力する
  printf("%d\n", watchmans);

  return 0;
}