You may be familiar with the concept of combinations: for example, if you take 5 cards from a 52 cards deck as you would playing poker, you can have a certain number (2,598,960, would you say?) of different combinations.

In mathematics the number of *k* combinations you can have taking from a set of *n* elements is called the [binomial coefficient](https://en.wikipedia.org/wiki/Binomial_coefficient) of n and k, more popularly called **n choose k**.

The formula to compute it is relatively simple: `n choose k`==`n!/(k!*(n-k)!)`, where `!` of course denotes the factorial operator.

You are now to create a choose function that computes the binomial coefficient, like this:

```
choose(1,1)==1
choose(5,4)==5
choose(10,5)==252
choose(10,20)==0
choose(52,5)==2598960
```

Be warned: a certain degree of optimization is expected, both to deal with larger numbers precision (and their rounding errors in languages like JS) and computing time.

```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 = 'import sys\nimport functools\nsys.setrecursionlimit(1_000_000)\n\n# lru_cache is a python shortcut for memoization\n# memoization is a technique to avoid repeatedly calculating\n# something that has already been calculated\n\n@functools.lru_cache(maxsize=1_000_000)\ndef choose(n,k):\n    # pascals triangle uses only addition\n    # so no rounding\n    #               1\n    #              1 1\n    #             1 2 1\n    #            1 3 3 1\n    #           1 4 6 4 1\n    # with exception of edge cases\n    # this has recursive formula\n    # choose(n, k) = choose(n-1, k-1) + choose(n-1, k)\n    if k > n:\n        return 0\n    if k == 0 or k == n:\n        return 1\n    return choose(n-1, k-1) + choose(n-1, k)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'choose'
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: 5606