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)

k = gets.split(" ")[1].to_i
i = gets.split("").map(&:to_i)
m = Array.new
i.count.times{|n|
if n == 0 then
   m.push([i[0],1])
else
    if i[n] == i[n-1] then
        next
    else
        m.push([i[n],n+1])
    end
    end
}
  m.push([0,i.count+1])
kotae = Array.new
m.count.times{|n|
a = n+2*k
if m[a]== nil then
    next
end
 
  if m[n][0]== 1 and m[a+1]== nil then
    next
  end
 
if m[n][0]== 0 then
    kotae.push(m[a][1] -m[n][1])
else
    kotae.push(m[a+1][1] -m[n][1])
end
}
print kotae.max
if kotae==[] then
  print i.count
end