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.*;
import java.io.*;

class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long K = sc.nextLong();
		long A = sc.nextLong();
		long B = sc.nextLong();

		long a=0;//hit my pocket
		long b=0;//bisquit to yen
		long c=0;//yen to biscuit
		if (A+1>=B) {
			System.out.println(K+1);
		}else {
			a+=K-A-1;
			K-=K-A-1;
			if (K%2==0) {
				b=K/2;
				c=K/2;
			}else if(K%2==1) {
				b=(K-1)/2;
				c=(K-1)/2;
				a++;
			}
			long bisquit = 1+a+(B-A)*b;
			System.out.println(bisquit);
		}
	}
}