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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    public static void main(String args[]) throws Exception{
        BufferedReader stdR = new BufferedReader(new InputStreamReader(System.in));
        String[] str = stdR.readLine().split(" ");
        long K = Long.parseLong(str[0]);
        long A = Long.parseLong(str[1]);
        long B = Long.parseLong(str[2]);
        if(A + 1 < B) {
            if(K <= A) {
                System.out.println(K + 1);
            }else {
                K = K - A + 1;
                System.out.println(A + (B - A) * (K / 2) + K % 2);
            }
        }else {
            System.out.println(1 + K);
        }
    }
}