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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

readInt :: String -> Int
readInt = read
x ? (a,b) = if x then a else b

main = do
    s <- map readInt.words<$>getContents
    print $ solve s

solve :: [Int] -> Int
solve = push 2

push 0 _ = 0
push n [a,b] = (a>b) ? (a + push (n-1) [a-1,b], b + push (n-1) [a,b-1])