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: Runtime Error)

# coding:utf-8

K, A, B = [int(i) for i in input().split()]

def cal(K, A, B):
    BNUM = 1
    TRANS_GET = B - A
    # 操作開始
    counter = 0
    while counter < K:
        nokori = K - counter
        if BNUM >= A:
        # 交換可能
            if nokori >= 2:
                syou = int(nokori / 2)
                amari = nokori % 2
                BNUM += TRANS_GET * syou + amari
                break
            else:
                BNUM += nokori
                break
        else:
        # 交換不可
            atonanko = A - BNUM
            if atonanko < nokori-2:
                BNUM += atonanko
                counter += atonanko
            else:
                BNUM += nikori
                break
    return BNUM


if A < B:
    if B - A > 2:
        max_b = cal(K, A, B)
    else:
        max_b = 1 + K
else:
    max_b = 1 + K

print(max_b)