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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.lang.*;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;
import java.math.BigInteger;

public class Main {
    static InputReader in = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int a = in.nextInt();
        int b = in.nextInt();
        if(Math.abs(a-b)>=2){
            if(a>b){
                out.println(a+(a-1));
            }
            else{
                out.println(b+(b-1));
            }
        }
        else{
            out.println(a+b);
        }
        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return null;
        }

        public boolean hasNext() {
            String next = null;
            try {
                next = reader.readLine();
            } catch (Exception e) {
            }
            if (next == null) {
                return false;
            }
            tokenizer = new StringTokenizer(next);
            return true;
        }

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }
    }
}