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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys

sys.setrecursionlimit(10 ** 5 + 10)


def input(): return sys.stdin.readline().strip()


def resolve():
    K, A, B = map(int, input().split())
    cnt = 0
    if B - A >= 3:
        times = (K - (A - 1)) // 2
        if times >= 1:
            cnt += A
            cnt+=(B-A)*times
            if (K - (A - 1)) // 2 == (K - (A - 1)) / 2:
                pass
            else:
                cnt += 1
        else:
            cnt = 1 + K
    else:
        cnt = 1 + K

    print(cnt)


resolve()