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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun f (a b n)
  (cond
    ((zerop n) 0)
    ((> a b) (+ a (f (1- a) b (1- n))))
    (t (+ b (f a (1- b) (1- n))))))

(let ((a (read))
      (b (read)))

  (format t "~A~%" (f a b 2)))