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 MINAPC2019
{
    class C
    {
        static void Main(string[] args)
        {
            long[] input = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long K = input[0];
            long A = input[1];
            long B = input[2];

            if (K < A)
            {
                Console.WriteLine(K + 1);
            }
            else if (A <= K)
            {
                if (B <= A) Console.WriteLine(K + 1);
                else if (A < B)
                {
                    long count = 1;
                    long ope = 0;
                    while (ope < K)
                    {
                        if (ope < K - 1 && A <= count && 2 <= B - A) { count -= A; count += B; ope += 2; }
                        else { count++; ope++; }
                        //Console.WriteLine("{0} {1}", ope, count);
                    }
                    Console.WriteLine(count);
                }
            }
        }
    }
}