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:\n     def flipLights(self, n, m):\n         """\n         :type n: int\n         :type m: int\n         :rtype: int\n         """\n         if m == 0:\n             return 1\n         lights = [True] * min(n, 3)\n         if m > 4:\n             if m & 1:\n                 m = 3\n             else:\n                 m = 4\n         return self.final(m, lights)\n         \n     def operate(self, num, array):\n         if num == 1:\n             array = [not i for i in array]\n         elif num == 2:\n             for i in range(len(array)):\n                 if i & 1:\n                     array[i] = not array[i]\n         elif num == 3:\n             for i in range(len(array)):\n                 if not i & 1:\n                     array[i] = not array[i]\n         elif num == 4:\n             for i in range(len(array)):\n                 if i%3 == 0:\n                     array[i] = not array[i]\n         return array\n \n     def final(self, num, array):\n         ops = [[[1] ,[2], [3], [4]],\n                [[], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]],\n                [[1] ,[2], [3], [4], [1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]],\n                [[], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4], [1, 2, 3, 4]]]\n         res = []\n         for op in ops[num-1]:\n             #print(op)\n             tmp = array.copy()\n             if not op:\n                 res.append(tmp)\n                 #print(\'  not op\')\n             else:\n                 #print(\'  op\')\n                 for i in op:\n                     tmp = self.operate(i, tmp)\n                 #print(\' \', tmp)\n                 if not tmp in res:\n                     res.append(tmp)\n         return len(res)\n'
_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: 9336