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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<iostream>
using namespace std;
int main() {
	int K, A, B;
	cin >> K >> A >> B;
	int maxnum=1;
	int sousakaisu = K;
	if (B - A < 3 || A >= K) {
		cout << K + 1;
		return 0;
	}
	else {
		maxnum += A-1;
		sousakaisu -= A-1;
		if (sousakaisu % 2 == 0) {
			maxnum += sousakaisu / 2 * (B - A);
		}
		else {
			maxnum += sousakaisu / 2 * (B - A) + 1;
		}
		cout << maxnum;
	}
}