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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String inputK = sc.next();
		String inputA = sc.next();
		String inputB = sc.next();

		int actionPoint = Integer.parseInt(inputK);
		int biscuitToMoneyRate = Integer.parseInt(inputA);
		int moneyToBiscuitRate = Integer.parseInt(inputB);

		int money = 0;
		int biscuit = 1;

		for(int i = 1; i <= actionPoint; i++) {
			if(money >= 1) {
				money -= 1;
				biscuit += moneyToBiscuitRate;
			}else if(moneyToBiscuitRate - biscuitToMoneyRate >= 3) {
				int remainingAP = actionPoint - i + 1;
				if(remainingAP >= 2) {
					if((remainingAP - 1) - (biscuitToMoneyRate - biscuit) > 0) {
						if(biscuit >= biscuitToMoneyRate) {
							biscuit -= biscuitToMoneyRate;
							money += 1;
						}else {
							biscuit += 1;
						}
					}else {
						biscuit += 1;
					}
				}else {
					biscuit += 1;
				}
			}else {
				biscuit += 1;
			}
		}

		System.out.println(biscuit);
		sc.close();
	}
}