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 Python (3.4.3) (judge verdict: Accepted)

#!/usr/bin/env python3
K, A, B = map(int, input().split())

if A + 2 >= B:
    print(K + 1)
    exit()

n = A - 1
print(1 + n + (K - n) // 2 * (B - A) + (K - n) % 2)

#  def f(n):
#      return (1 + n) // A <= (K - n) // 2
#
#
#  ok = 0
#  ng = int(10**9 + 1)
#  while ng - ok > 1:
#      m = (ok + ng) // 2
#      if f(m):
#          ok = m
#      else:
#          ng = m
#
#  print(1 + ok + (B - A) * ((1 + ok) // A))