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: Runtime Error)

n,k = gets.split(" ").map(&:to_i)
s = gets.chomp

a = s.split('0').map(&:length)
b = s.split('1').map(&:length)
a.delete(0)
b.delete(0)

c = []
c << 0 if s[0] == '0'
while !a.empty? || !b.empty? do
  c << a.shift unless a.empty?
  c << b.shift unless b.empty?
end

r = [0]
c.size.times do |i|
  r[i + 1] = r[i] + c[i]
end

ans = 0

0.step(by: 2, to: c.size) do |i|
  left = i
  right = [(i + 2 * k + 1), c.size].min
  tmp = r[right] - r[left]

  ans = [tmp, ans].max
end
puts ans