There is a room with n lights which are turned on initially and 4 buttons on the wall. After performing exactly m unknown operations towards buttons, you need to return how many different kinds of status of the n lights could be.



Suppose n lights are labeled as number [1, 2, 3 ..., n], function of these 4 buttons are given below:


Flip all the lights.
Flip lights with even numbers.
Flip lights with odd numbers.
Flip lights with (3k + 1) numbers, k = 0, 1, 2, ...




Example 1:

Input: n = 1, m = 1.
Output: 2
Explanation: Status can be: [on], [off]




Example 2:

Input: n = 2, m = 1.
Output: 3
Explanation: Status can be: [on, off], [off, on], [off, off]




Example 3:

Input: n = 3, m = 1.
Output: 4
Explanation: Status can be: [off, on, off], [on, off, on], [off, off, off], [off, on, on].



Note:
n and m both fit in range [0, 1000].

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'class Solution(object):\n \tdef flipLights(self, lightNum, performTime):\n \t\tif(lightNum == 0):\n \t\t\treturn(0)\n \n \t\tif(performTime == 0):\n \t\t\treturn(1)\n \n \t\tif(lightNum == 1):\n \t\t\treturn(2)\n \n \t\tstatuNumToStatu = dict()\n \t\tstatuNumToStatu[0] = (False,)*lightNum\n \t\tstatuNumToStatu[1] = (True,)*lightNum\n \t\tstatuNumToStatu[2] = tuple(True if(i%2 == 0) else False for i in range(1,lightNum+1))\n \t\tstatuNumToStatu[3] = tuple(True if(i%2 == 1) else False for i in range(1,lightNum+1))\n \t\tstatuNumToStatu[4] = tuple(True if(i%3 == 1) else False for i in range(1,lightNum+1))\n \t\tstatuNumToStatu[4] = tuple(True if(i%3 == 1) else False for i in range(1,lightNum+1))\n \t\tstatuNumToStatu[(1,4)] = tuple(True if(i%3 != 1) else False for i in range(1,lightNum+1))\n \t\tstatuNumToStatu[(2,4)] = tuple(True if((i%2 == 0)^(i%3 == 1)) else False for i in range(1,lightNum+1))\n \t\tstatuNumToStatu[(3,4)] = tuple(True if((i%2 == 1)^(i%3 == 1)) else False for i in range(1,lightNum+1))\n \n \t\t# for key in statuNumToStatu:\n \t\t\t# print(key,statuNumToStatu[key])\n \n \t\tstatuNumToNextStatuNums = {\n \t\t\t0:[1,2,3,4],\n \t\t\t1:[0,2,3,(1,4)],\n \t\t\t2:[0,1,3,(2,4)],\n \t\t\t3:[0,1,2,(3,4)],\n \t\t\t4:[0,(1,4),(2,4),(3,4)],\n \t\t\t(1,4):[1,4,(2,4),(3,4)],\n \t\t\t(2,4):[2,4,(1,4),(3,4)],\n \t\t\t(3,4):[3,4,(1,4),(2,4)],\n \t\t}\n \n \t\tprevStatuNums = {0}\n \t\tfor eachTime in range(performTime):\n \t\t\tnextStatuNums = set()\n \t\t\tfor eachStatuNum in prevStatuNums:\n \t\t\t\tfor eachNextStatu in statuNumToNextStatuNums[eachStatuNum]:\n \t\t\t\t\tnextStatuNums.add(eachNextStatu)\n \n \t\t\tprevStatuNums = nextStatuNums\n \n \t\tallStatus = set()\n \t\tfor eachStatuNum in prevStatuNums:\n \t\t\tallStatus.add(statuNumToStatu[eachStatuNum])\n \n \t\treturn(len(allStatus))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'flipLights'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6324