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 Rust (1.15.1) (judge verdict: Accepted)

mod stdin_reader {
  use std::io::stdin;
  use std::io::Read;

  pub struct StdinReader {
    pub buf: Vec<String>,
    pub cursor: usize,
  }

  pub fn new() -> StdinReader {
    StdinReader::new()
  }

  impl StdinReader {
    pub fn new() -> Self {
      let mut s = String::new();
      let stdin = stdin();
      stdin.lock().read_to_string(&mut s).unwrap();
      let buf = s.split_whitespace().map(|s| s.to_string()).collect();
      return StdinReader { buf: buf, cursor: 0 }
    }

    pub fn read_all(&self) -> Vec<String> {
      return self.buf.clone()
    }

    pub fn next(&mut self) -> Option<String> {
      let val = self.buf.get(self.cursor).cloned();
      self.cursor += 1;
      return val
    }

    pub fn as_i64(&mut self) -> Option<i64> {
      self.next().and_then(|s| s.parse::<i64>().ok())
    }

    pub fn as_f64(&mut self) -> Option<f64> {
      self.next().and_then(|s| s.parse::<f64>().ok())
    }

    pub fn as_usize(&mut self) -> Option<usize> {
      self.next().and_then(|s| s.parse::<usize>().ok())
    }
  }
}

mod utils {
  pub fn is_int(n: f64) -> bool {
    let trunc = (n.trunc() as i64) as f64;
    return (n - trunc) < 0.0001
  }
}

fn main() {
  // stdout
  use std::io::{stdout, Write, BufWriter};
  let stdout = stdout();
  let mut writer = BufWriter::new(stdout.lock());

  // stdin
  let mut reader = stdin_reader::new();

  let n = reader.as_f64().unwrap();
  let d = reader.as_f64().unwrap();
  println!("{}", (n / (1.0+2.0*d)).ceil() as i64)
}