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.Linq;

namespace PictureManagement
{
    class Program
    {
        static void Main(string[] args)
        {
            var sp = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            Solution sol = new Solution();
            Console.WriteLine(sol.GetMaxBiscuit(sp[0], sp[1], sp[2]));
        }
    }

    public class Solution
    {
        public long GetMaxBiscuit(long K, long A, long B)
        {
            if (B - A - 2 <= 0 || K < A)
                return K + 1;

            long biscuit = A;
            K = K - A + 1;
            while(true)
            {
                if (K >= 2)
                    biscuit += B - A;
                else
                    break;
                K -= 2;
            }

            return biscuit + K;
        }
    }
}