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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using BI = System.Numerics.BigInteger;

class Program
{
	public static void Main(String[] args)
	{
		// スペース区切りの整数の入力
		var input = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
		long K = input[0];
		long A = input[1];
		long B = input[2];

		long money = 0;
		long bisketNum = 1;
		if (A + 1 >= B)
			bisketNum += K;
		else
		{
			long changeTarget = K - A + 1;
			long changeNum = changeTarget / 2;
			long other = changeTarget % 2;

			bisketNum = changeNum * B + other;
		}

		Console.WriteLine(bisketNum);
	}
}