Problem:
Score : 100 points

Problem Statement

There are two buttons, one of size A and one of size B.

When you press a button of size X, you get X coins and the size of that button decreases by 1.

You will press a button twice. Here, you can press the same button twice, or press both buttons once.

At most how many coins can you get?

Constraints

All values in input are integers.

3 \leq A, B \leq 20

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of coins you can get.

Sample Input 1

5 3

Sample Output 1

9

You can get 5 + 4 = 9 coins by pressing the button of size 5 twice, and this is the maximum result.

Sample Input 2

3 4

Sample Output 2

7

Sample Input 3

6 6

Sample Output 3

12

Solution in Python (3.4.3) (judge verdict: Runtime Error)

class BufInput:
  def __init__(self):
    self.save = False
    self.buf = None
  def read(self, save=False):
    if self.save:
      ret = self.buf
    else:
      try:
        ret = input()
      except EOFError as e:
      	ret = None
    self.save = save
    self.buf = ret
    return ret
    
  
bi = BufInput()
while bi.read(True):
  n, k = map(int, bi.read().split())
  s = bi.read().rstrip()

  def findEx(s, f, pos, notfound):
    pos = s.find(f, pos)
    if pos == -1:
      pos = notfound
    return pos

  ans = 0
  left = 0
  right = 0
  while right < n:
      if k > 0:
          right = findEx(s, '01', right, n-1) + 1
          k = k - 1
          right = findEx(s, '10', right, n-1) + 1
          ans = max(ans, right - left)
      else:
          left = findEx(s, '01', left, n-1) + 1
          k = k + 1

  print(ans)