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: Accepted)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		new Main().solve(new Scanner(System.in));
	}
	
	public void solve(Scanner sc) {
		long k = Integer.parseInt(sc.next());
		long a = Integer.parseInt(sc.next());
		long b = Integer.parseInt(sc.next());
		
		if(a >= b - 2) {
			System.out.println(k+1);
			return;
		}
		
		long bisk = 1;
		long money = 0;
		while(k>0) {
			if(money >= 1) {
				money--;
				bisk += b;
			} else if(k>=2 && bisk>=a) {
				bisk -= a;
				money++;
			} else {
				bisk++;
			}
			k--;
		}
		System.out.println(bisk);
	}
}