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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static ABC.Cin;
using static ABC.Cout;
using static ABC.Tool;


namespace ABC
{
    class Program
    {
        static void Main(string[] args)
        {
            Scanf(out long k, out long a, out long b);

            var ans = 1L;
            if(k < a)
            {
                OutL(k);
                return;
            }

            ans += a - 1;
            var left = k - (a - 1);
            if(left % 2 == 1)
            {
                left--;
                ans++;
            }

            if(b - a > 2)
            {
                ans += (left / 2) * (b - a);
            }
            else
            {
                ans += left;
            }
            OutL(ans);
        }
    }

    static class Cin
    {
        public static string[] ReadSplit => Console.ReadLine().Split();
        public static int[] ReadSplitInt => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] ReadSplitLong => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string Str => Console.ReadLine();
        public static int Int => int.Parse(Console.ReadLine());
        public static long Long => long.Parse(Console.ReadLine());
        public static double Double => double.Parse(Console.ReadLine());
        public static T Conv<T>(string input)
        {
            return (T)Convert.ChangeType(input, typeof(T));
        }
        public static void Scanf<T>(out T a) => a = Conv<T>(Console.ReadLine());
        public static void Scanf<T,U>(out T a, out U b)
        {
            var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]);
        }
        public static void Scanf<T, U, V>(out T a, out U b, out V c)
        {
            var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]);
        }
        public static void Scanf<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); d = Conv<W>(q[3]);
        }
    }
    static class Cout
    {
        public static void OutL(object s) => Console.WriteLine(s);
    }
    static class Tool
    {
        public static long Gcd(long a, long b)
        {
            if (a % b == 0)
            {
                return b;
            }
            else
            {
                return Gcd(b, a % b);
            }
        }
        public static long Lcm(long a, long b) => a * b / Gcd(a, b);

        public static long[] PrimeFac(long n)
        {
            var result = new long[n + 1];
            for(int i = 2; i * i <= n; i++)
            {
                if (n % i != 0)
                {
                    continue;
                }

                var cnt = 0;
                while(n % i == 0)
                {
                    cnt++;
                    n /= i;
                }
                result[i] = cnt;
            }
            if(n != 1)
            {
                result[n] = 1;
            }
            return result;
        }
        public static long DivsCnt(long n)
        {
            var result = 1L;
            for (int i = 2; i * i <= n; i++)
            {
                if (n % i != 0)
                {
                    continue;
                }

                var cnt = 0;
                while (n % i == 0)
                {
                    cnt++;
                    n /= i;
                }
                result *= (cnt + 1);
            }
            if (n != 1)
            {
                result *= 2;
            }
            return result;
        }

        public static string Reversed(string s)
        {
            return string.Join("", s.Reverse());
        }
    }
}