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 Python (3.4.3) (judge verdict: Accepted)

import sys
sys.setrecursionlimit(4100000)

import logging

logging.basicConfig(level=logging.DEBUG)

logger = logging.getLogger(__name__)


def resolve():
    N, D = [int(x) for x in sys.stdin.readline().split()]

    logger.debug('{} {}'.format(N, D))

    def ceil_int(a, devider):
        """
        floor は a // devider でいい。
        math.floor(a / divedier)　だとオーバーフローしちゃう。
        """

        if (a % devider > 0):
            a_ceil = a // devider + 1
        else:
            a_ceil = a // devider

        return a_ceil

    print(ceil_int(N, 2 * D + 1))


if __name__ == "__main__":
    resolve()

# AtCoder Unit Test で自動生成できる, 最後のunittest.main は消す
# python -m unittest template/template.py で実行できる
# pypy3 -m unittest template/template.py で実行できる

import sys
from io import StringIO
import unittest


class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)

    def test_入力例_1(self):
        input = """6 2"""
        output = """2"""
        self.assertIO(input, output)

    def test_入力例_2(self):
        input = """14 3"""
        output = """2"""
        self.assertIO(input, output)

    def test_入力例_3(self):
        input = """20 4"""
        output = """3"""
        self.assertIO(input, output)

    def test_入力例_4(self):
        input = """1 1"""
        output = """1"""
        self.assertIO(input, output)