Contest Duration: - (local time) (100 minutes) Back to Home
B - Golden Apple /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

そこで、何人かの監視員を配置してどの林檎の木もいずれかの監視員に監視された状態にしたいです。

それぞれの監視員は N 本の木のうちいずれかに配置します。便宜上、これらの木に 1 から N までの番号をつけます。番号 i の木に配置された監視員は、番号が i-D 以上 i+D 以下のすべての林檎の木を監視します。

### 制約

• 入力は全て整数である。
• 1 \leq N \leq 20
• 1 \leq D \leq 20

### 入力

N D


### 入力例 1

6 2


### 出力例 1

2


### 入力例 2

14 3


### 出力例 2

2


### 入力例 3

20 4


### 出力例 3

3


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