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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ProConCWhenIHitMyPocket
{
    class Program
    {
        static void Main(string[] args)
        {
            // 整数の入力
            //int a = int.Parse(Console.ReadLine());
            // スペース区切りの整数の入力
            string[] input = Console.ReadLine().Split(' ');
            long K = long.Parse(input[0]);
            long A = long.Parse(input[1]);
            long B = long.Parse(input[2]);
            // 文字列の入力
            //string s = Console.ReadLine();
            long biscuit = 1;
            long yen = 0;
            if (B <=( A+2))
            {
                biscuit = 1 + K;
            }
            else
            {
                for (long i = 1; i <= K; i++)
                 {
                    if (yen ==1)
                    {
                    yen = 0;
                    biscuit += B;
                        //Console.WriteLine("ビスケットをB個　買い足しました。");
                        continue;
                    }
                    else if ((biscuit >= A ) && (i < K))
                    {
                    biscuit -=A;
                    yen++;
                        //Console.WriteLine("円に換えました。");
                    continue;
                    }
                    else
                    {
                        biscuit++;
                    }
                }
               
            }
            //出力
                   Console.WriteLine(biscuit);
        }
    }
}