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

namespace Atcoder
{
    class AtCodeeeeeeeeeeeeeeeeeeeer
    {
        static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split(' ');
            long K = long.Parse(s[0]);
            long A = long.Parse(s[1]);
            long B = long.Parse(s[2]);
            long Biscuit = 1;
            long umami = 0;
            for (int i = 1; i <= K; i++)
            {
                umami = B - A;
                if (umami > 2)
                {
                    if((K - i)+1>=2 && Biscuit >= A)
                    {
                        Biscuit += umami;
                        i++;//2ターン消費させる
                    }
                    else
                    {
                        Biscuit++;
                    }
                }
                else
                {
                    Biscuit++;
                }
            }
            Console.WriteLine(Biscuit);
        }
    }
}