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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.util.Scanner

object Main {
  def main(args: Array[String]) = {
    val sc = new Scanner(System.in)
    val A, B = sc.nextInt()
    val c = A.max(B) + A.max(B) - 1
    
    def foo(a: Int, b: Int, sum: Int = 0, deps: Int = 1): Int = {
      if (deps == 0) sum else {
        if (a < b) {
          foo(a, b - 1, b, deps - 1)
        } else {
          foo(a - 1, b, a, deps - 1)
        }
      }
    }
    
    foo(A, B)
    println(c)
  }
}