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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using E = System.Linq.Enumerable;
class Program
{
    static char[] abc = "abcdefghijklmnopqrstuvwxyz".ToCharArray();
    static long mod = 1000000007;
    static void Main(string[] args)
    {
        var AKB = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var K = AKB[0];
        var A = AKB[1];
        var B = AKB[2];
        var ans = K+1;
        if(A < B)
        {
            ans = Math.Max(ans,A+(B-A)*((K - A + 1)/2) + (K - A + 1) % 2);
        }

        Console.WriteLine(ans);
    }
        

    
}