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;

public class Hello
{
    public static void Main()
    {
        
        int[] a = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        int K = a[0];
        int A = a[1];
        int B = a[2];
        long num = 1;
        int i = 1;
        bool flag = false; //A枚を1円に交換したらfalseにする
        while(i <= K)
        {
            
            if(B - A < 2)
            {
                num ++;
                i++;
                
            }
            else if(B - A >= 2)
            {
                
                if(num >= A && i <= K-1)
                {
                    num -= A;
                    num += B;
                    i += 2;
                    
                    
                }
                else
                {
                    num++;
                    i++;
                
                }
            }
        }
        
        Console.WriteLine(num);
    }
}