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) {
        final Scanner scan = new Scanner(System.in);
        long K = scan.nextInt();
        final long A = scan.nextInt();
        final long B = scan.nextInt();

        long biscuit = 1;
        long jpy = 0;

        if (B - A <= 2) {
            while (K > 0) {
                biscuit++;
                K--;
            }
            System.out.println(biscuit);
            return;
        }

        while (K > 0) {
            if (jpy > 0) {
                jpy--;
                biscuit += B;
                K--;
                continue;
            }

            if (biscuit < A || K < A) {
                biscuit++;
                K--;
                continue;
            }
            if (biscuit >= A) {
                biscuit = biscuit - A;
                jpy++;
                K--;
            }
        }
        System.out.println(biscuit);
    }
}