*This is the advanced version of the 
[Minimum and Maximum Product of k Elements](https://www.codewars.com/kata/minimum-and-maximum-product-of-k-elements/) kata.*

---

Given a list of **integers** and a positive integer `k` (> 0), find the minimum and maximum possible product of `k` elements taken from the list.

If you cannot take enough elements from the list, return `None`/`nil`.

## Examples

```python
numbers = [1, -2, -3, 4, 6, 7]

k = 1  ==>  -3, 7
k = 2  ==>  -21, 42    # -3*7, 6*7
k = 3  ==>  -126, 168  # -3*6*7, 4*6*7
k = 7  ==>  None       # there are only 6 elements in the list
```

Note: the test lists can contain up to 500 elements, so a naive approach will not work.

---

## My other katas

If you enjoyed this kata then please try [my other katas](https://www.codewars.com/collections/katas-created-by-anter69)! :-)

#### *Translations are welcome!*

```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 = 'from functools import reduce\nfrom typing import List, Optional, Tuple\n\ndef find_min_max_product(arr: List[int], kpi: int) -> Optional[Tuple[int, int]]:\n\n    if kpi <= len(arr):\n        mul = []\n        arr.sort()\n        for _ in range(kpi):\n            mul.append(reduce(lambda x, y: x * y, arr[0:kpi], 1))\n            mul.append(reduce(lambda x, y: x * y, arr[-kpi:], 1))\n            arr = [arr[-1]] + arr[:-1]\n        return min(mul), max(mul)\n    return None'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'find_min_max_product'
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: 6034