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 <iomanip>
#include <string>
#include <cmath>
#include <climits>
#include <algorithm>
#include <cassert>
#include <vector>
#include <array>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <stack>
#include <queue>
#include <numeric>
#define ALL(c) (c).begin(), (c).end()

using namespace std;
using ll = long long;
using pli = pair<ll, int>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdi = pair<double, int>;
using pdd = pair<double, double>;

int K, A, B;

int main() {
	cin >> K >> A >> B;
	ll ans = 1;
	if (B - A <= 2) {
		ans += K;
	}
	else {
		K -= A - 1;
		if (K <= 0) {
			ans += K;
		}
		else {
			ans += A - 1;
			const int s = B - A;
			ans += (ll)K / 2 * s;
			K %= 2;
			if (K == 1) {
				ans++;
			}
		}
	}
	cout << ans << endl;
	return 0;
}