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 (GCC 5.4.1) (judge verdict: Accepted)

/* ex4_1
   moka223711 */

#include <stdio.h>

int main(void){
    // n本の木があり、1〜nの番号がついている
    // 番号iの木に監視員がつき、i-dからi+dまでの木を監視できる
    // すべての木を監視するのに必要な監視員の数の最小値を求める
    
    int n, d, ans = 0;
    scanf("%d %d", &n, &d);
    
    // 監視員はi-dからi+dまでの2d+1本の木を監視できる
    // nを2d+1で割った商を求め、余りがあったときはもう一人監視員を加える
    ans = n / (2*d + 1);
    if(n % (2*d + 1) != 0){
        ans++;
    }
    printf("%d\n", ans);
    
    return 0;
}