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 (2.3.3) (judge verdict: Wrong Answer)

k, a, b = gets.split(' ')
k = k.to_i ; a = a.to_i ; b = b.to_i
cookie = 1
if (b - a) <= 1 || (a - k) >= 1
  cookie = cookie + k
elsif a == k
  cookie = b
elsif (a - k) == -1
  cookie = [b,k+1].max
else
  # step 1
  k = k - (a - 1)
  cookie = cookie + (a - 1)
  
  # step 2
  k = k - 1

  # step 3
  k = k - 1
  cookie = b
  
  # step 3
  cookie = cookie + ((b - a) * (k / 2))
  cookie = cookie + 1 if k.odd?
end

puts cookie