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)

k, a, b = map(int, input().split())

# ビスケットの売値が買値より安い場合
if a+2 > b:
    print(1 + k)
    exit()

# 交換獲得に必要なターン数
roop_turn = a+2

# 初回時ビスケット１枚を余分に所持
if k < roop_turn-1:
    print(1 + k)
    exit()

# 獲得ビスケット
ret = b

# 残りターン
remaining = k - (roop_turn-1)

q, mod = divmod(remaining, 2)

ret += (b-a)*q + mod
print(ret)