Problem:
Score : 400 points

Problem Statement

Snuke has one biscuit and zero Japanese yen (the currency) in his pocket.
He will perform the following operations exactly K times in total, in the order he likes:

Hit his pocket, which magically increases the number of biscuits by one.

Exchange A biscuits to 1 yen.

Exchange 1 yen to B biscuits.

Find the maximum possible number of biscuits in Snuke's pocket after K operations.

Constraints

1 \leq K,A,B \leq 10^9

K,A and B are integers.

Input

Input is given from Standard Input in the following format:

K A B

Output

Print the maximum possible number of biscuits in Snuke's pocket after K operations.

Sample Input 1

4 2 6

Sample Output 1

7

The number of biscuits in Snuke's pocket after K operations is maximized as follows:

Hit his pocket. Now he has 2 biscuits and 0 yen.

Exchange 2 biscuits to 1 yen. his pocket. Now he has 0 biscuits and 1 yen.

Hit his pocket. Now he has 1 biscuits and 1 yen.

Exchange 1 yen to 6 biscuits. his pocket. Now he has 7 biscuits and 0 yen.

Sample Input 2

7 3 4

Sample Output 2

8

Sample Input 3

314159265 35897932 384626433

Sample Output 3

48518828981938099

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

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long[] hi;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var KAB = Sarray();
            var K = KAB[0];
            var A = KAB[1];
            var B = KAB[2];
            //交換するより増やす方が良い
            if (B <= A + 2)
            {
                WriteLine(1 + K);
                return;
            }
            //A 枚まで増やせない
            if(K <= (A - 1))
            {
                WriteLine(K + 1);
                return;
            }
            var zan = K - (A - 1);
            //交換する。1円→B枚のセット
            if (zan == 1)//そのまま増やす
            {
                WriteLine(K + 1);
                return;
            }
            if (zan == 2)//A→1→B
            {
                WriteLine(B);
                return;
            }
            var ans = B + (zan - 2) / 2 * (B - A) + (zan - 2) % 2;
            WriteLine(ans);
            //Out.Flush();
        }
    }
}