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: Wrong Answer)

def solve(k, a, b):
    if b <= a + 1:
        return 1 + k
    # init
    c = 0
    k += 1
    # c = a ?
    if k <= a + 2:
        return k
    c = 0
    k -= a + 1
    num_iter, rest = divmod(k, 2)
    if rest == 0:
        # ends (2)
        c += (num_iter - 1) * (b - a)
        c += b + 1
    else:
        c += num_iter * (b - a) + b
    return c


    


def main():
    k, a, b = (int(z) for z in input().split())
    res = solve(k, a, b)
    print(res)


if __name__ == "__main__":
    main()