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;
using System.Diagnostics;

class Program
{

    public void Slove()
    {   
        var inputs = Console.ReadLine().Split();
        int k = int.Parse(inputs[0]);
        int sellRate = int.Parse(inputs[1]);
        int buyRate = int.Parse(inputs[2]);
        int add = buyRate - sellRate;
        if(add <= 2)
        {
            Console.WriteLine(k + 1);
            return;
        }
        int sbCount = (k - sellRate + 1) / 2;
        long biscuit = (long)sbCount * add + 1 + (k - sbCount * 2);

        Console.WriteLine(biscuit);

    }
    static void Main(string[] args)
    {
        var p = new Program();
        p.Slove();
    }
}