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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

/**
 *  Name: Chris M. Perez
 *  University: Interamerican University Metro Campus
 *
**/

#define endl '\n'
#define MOD 10E9
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define gcd(x , y) __gcd(x , y)
#define all(x) (x).begin() , (x).end()
#define forn(i , a , b) for(int i=(a);i<(b);i++)
#define forrange(j , a , b) for(int j=(a);j<=(b);j++)
#define nestedforn(i , a , b , j , c , d) for(int i=(a);i<=(b);i++) for(int j=(c);j<=(d);j++)
#define sort_all(x) sort(all(x))
#define zeros_at_beginning(x) __builtin_clz(x)
#define zeros_at_end(x) __builtin_ctz(x)
#define ones(x) __builtin_popcount(x)
#define parity_even_or_odd_ones __builtin_parity(x)
#define PI 3.141592653589793

template<class T> bool minn(T &a ,T b){ return (a > b ? (a = b , true) : false); };
template<class T> bool maxn(T &a ,T b){ return (a < b ? (a = b , true) : false); };

                                     
int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.precision(10);
  cout << fixed;  

#ifdef LOCAL_DEFINE
  freopen("input.txt" , "rt" , stdin);
#endif

  double n; cin >> n;
  double d; cin >> d;
  cout << ceil(n / ((d * 2) + 1)) << endl;
                                             
#ifdef LOCAL_DEFINE 
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif  
  return 0;
}