-----Problem Statement-----
Harry Potter has one biscuit and zero rupee 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 $1$ rupee.
- Exchange $1$ rupee to $B$ biscuits.
Find the maximum possible number of biscuits in Harry's pocket after $K$ operations.

-----Input-----
Input is given in the following format:
K A B

-----Output-----
Print the maximum possible number of biscuits in Harry's pocket after $K$operations.

-----Constraints-----
- $1 \leq K, A, B \leq 10^9$
- $K$, $A$ and  are integers.

-----Sample Input-----
4 2 6

-----Sample Output-----
7

-----EXPLANATION-----
The number of biscuits in Harry's pocket after $K$ operations is maximized as follows:
- Hit his pocket. Now he has $2$ biscuits and $0$ rupee.
- Exchange $2$ biscuits to $1$ rupee in his pocket .Now he has $0$ biscuits and $1$ rupee.
- Hit his pocket. Now he has $1$ biscuits and $1$ rupee.
- Exchange $1$ rupee to $6$ biscuits. his pocket. Now he has $7$ biscuits and $0$ rupee.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\nimport math\n#from queue import *\nimport random\n#sys.setrecursionlimit(int(1e6))\ninput = sys.stdin.readline\n \n############ ---- USER DEFINED INPUT FUNCTIONS ---- ############\ndef inp():\n    return(int(input()))\ndef inara():\n    return(list(map(int,input().split())))\ndef insr():\n    s = input()\n    return(list(s[:len(s) - 1]))\ndef invr():\n    return(list(map(int,input().split())))\n################################################################\n############ ---- THE ACTUAL CODE STARTS BELOW ---- ############\n\nk,a,b=invr()\n\nif k<a-1:\n\tprint(1+k)\n\treturn\n\nnow=a\nk-=(a-1)\n\nif b-a>=3:\n\tnow=a+(k//2)*(b-a)+k%2\nelse:\n\tnow=a+k\n\nprint(now)\n\t\n\t\t\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: