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.Minpro2019_2_9
{
    class C
    {
        public static void Solve()
        {
            var s = Console.ReadLine().Split();
            var k = ulong.Parse(s[0]);
            var a = ulong.Parse(s[1]);
            var b = ulong.Parse(s[2]);

            if(b <= a + 1 || k <= a)
            {
                Console.WriteLine(k + 1);
                return;
            }
            
            ulong ans = (b-a) * ((k - (a - 1)) / 2) + (k - (a - 1)) % 2 + a;
            Console.WriteLine(ans);
        }
    }
}
namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            Minpro2019_2_9.C.Solve();
        }
    }
}