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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>

using namespace std;


void solve()
{
	long long int K, A, B;
	cin >> K >> A >> B;
	if (A + 2 >= B)
	{
		cout << K + 1 << endl;
		return;
	}
	long long int has = 1;
	if (K - has >= A)
	{
		K -= A - has;
		has = A;
	}
	else
	{
		has += K;
		K = 0;
	}
	if (has >= A)
	{
		if (K >= 2)
		{
			has -= A;
			has += B;
			K -= 2;
		}
		else if(K == 1)
		{
			has++;
			K--;
		}
	}
	has += (B - A) * (K / 2);
	if (K % 2 == 1)
	{
		has++;
	}
	cout << has << endl;
}

int main()
{
	solve();
	return(0);
}