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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.List;
import java.util.stream.Collectors;

class Main {

    public static void main(String[] args) throws Exception {

        try {

            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

            List<String> input = Arrays.asList(br.readLine().split(" "));
            input = input.stream().sorted(Comparator.naturalOrder()).collect(Collectors.toList());

            int countOfCoinA = Integer.parseInt(input.get(0));
            int countOfCoinB = Integer.parseInt(input.get(1));

            int result = countOfCoinA + countOfCoinB;
            if (result < countOfCoinB * 2 - 1) {
                result = countOfCoinB * 2 - 1;
            }

            System.out.println(result);
        } catch (IOException | NumberFormatException e) {
            e.printStackTrace();
            System.exit(0);
        } catch (final Exception e) {
            e.printStackTrace();
            System.exit(0);
        }
    }
}