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 Ruby (2.7.1) (judge verdict: Accepted)

k, a, b = gets.chomp.split.map(&:to_i)
bis = 1
if a + 2 >= b
  puts k + bis
else
  loop do
    if k <= 0
      break
    end

    if bis >= a && k > 1
      cnt = [k / 2, bis / a].min
      bis += (b - a) * cnt
      k -= 2 * cnt
    elsif k == 1
      bis += 1
      k -= 1
    else
      cnt = [k, [0, a - bis].max].min
      bis += cnt
      k -= cnt
    end
  end
  puts bis
end