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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using static kyoupuro.Input;
using static kyoupuro.MyMath;

namespace kyoupuro {

    class MainClass {

        public static void Main() {
            var a = NextInt();
            var b = NextInt();
            var count = 0;
            if(a > b) {
                count += a;
                a--;
            } else {
                count += b;
                b--;
            }
            if (a > b) {
                count += a;
                a--;
            } else {
                count += b;
                b--;
            }

            Console.WriteLine(count);
        }
    }

    class MyMath {
        public const long mod = 1000000007;

        public static long Gcd(long a, long b) {
            return b == 0 ? a : Gcd(b, a % b);
        }

        public static List<long> Factor(long n) {
            var list = new List<long>();
            n = DivideToLimit(n, 2, list);
            n = DivideToLimit(n, 3, list);
            long sqrt = Sqrt(n);
            for (int i = 5; i <= n && i <= sqrt; i += 4) {
                n = DivideToLimit(n, i, list);
                i += 2;
                n = DivideToLimit(n, i, list);
            }
            if (n > 1) list.Add(n);
            return list;
        }

        public static long Sqrt(long n) {
            if (n < 0) return 0;
            long a = 0, tmp = 0, b = 0;
            for (int i = 62; i >= 0; i -= 2) {
                tmp = (b << 1) + 1 <= (n >> i) ? 1 : 0;
                a = a << 1 | tmp;
                n -= (((b << 1) + 1) * tmp) << i;
                b = (b << 1) + tmp + tmp;
            }
            return a;
        }

        static long DivideToLimit(long divisor, long dividend, List<long> list) {
            while (divisor % dividend == 0) {
                list.Add(dividend);
                divisor /= dividend;
            }
            return divisor;
        }
    }

    class Input {
        static IEnumerator<string> enumerator = new string[] { }.AsEnumerable().GetEnumerator();

        public static string Line() {
            return Console.ReadLine();
        }

        public static int NextInt() {
            while (!enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
            }
            return int.Parse(enumerator.Current);
        }

        public static long NextLong() {
            while (!enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
            }
            return long.Parse(enumerator.Current);
        }

        public static string[] StrArr() {
            return Line().Split(' ');
        }

        public static List<int> IntList() {
            return StrArr().Select(int.Parse).ToList();
        }

        public static List<long> LongList() {
            return StrArr().Select(long.Parse).ToList();
        }

        public static void Skip(int line = 1) {
            enumerator.Reset();
            for (int i = 0; i < line; i++) Console.ReadLine();
        }

        public static void Reset() {
            enumerator.Reset();
        }
    }
}