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
   takafumi_ueki */
#include <stdio.h>
#include <math.h>
int main(void){
    double tree_num,watch_num,tree_range;
    int count;
    //tree_num(木の本数)とwatch_num(監視員の数)を受け取る
    scanf("%lf %lf",&tree_num,&watch_num);
    //監視員が見れる木の本数を計算する
    tree_range = 2*watch_num + 1;
    //「全ての木の本数」を「監視員が見れる木の本数」で割り、割り切れない場合は一人追加する
    count = ceil(tree_num/tree_range);
    printf("%d\n",count);
    return 0;
}