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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.math._
import scala.annotation._
import scala.collection._
import scala.collection.{mutable => mut}
import scala.util.control.Breaks.{breakable,break}

object Main {
  def main(args: Array[String]) {
    val sc = new java.util.Scanner(System.in)

    val k, a, b = sc.nextLong
    val l = k + 1

    val m =
      if (a + 2 >= b)
        l
      else {
        val l_ = l - a
        a + l_ / 2 * (b - a) + l % 2
      }
    println(m)
  }
}