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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n, k = gets.split(' ').map{|a|a.to_i}
s = gets.to_s.chomp

que = []
counter = ''
s.chars.each do | c |
  if counter == ''
    counter = c
    next
  end
  if counter[0] == c
    counter = counter + c
  else
    que << counter.size
    counter = c
  end
end
que << counter.size if counter.size > 0

max = 0
len = 2*k+1
0.upto(que.size-1) do | i |
  nums = que.slice(i, len)
  sum = 0
  nums.each do | num |
    sum += num
  end
	max = sum if sum > max
end
puts max