




def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> Optional[Any]:
       lowerCamelCase   :      Tuple			 =					[0 for i in range(r + 1    )]
       # nc0 = 1
       lowerCamelCase   :      Optional[int]			 =					1
       for i in range(1 ,n + 1    ):
              # to compute current row from previous row.
              lowerCamelCase   :      List[str]			 =					min(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
              while j > 0:
                     c[j] += c[j - 1]
                     j -= 1
       return c[r]


print(binomial_coefficient(n=10, r=5))







"""simple docstring"""







import sys

from .dependency_versions_table import deps
from .utils.versions import require_version, require_version_core


# define which module versions we always want to check at run time
# (usually the ones defined in `install_requires` in setup.py)
#
# order specific notes:
# - tqdm must be checked before tokenizers

__SCREAMING_SNAKE_CASE    	="python tqdm regex requests packaging filelock numpy tokenizers".split()
if sys.version_info < (3, 7):
       pkgs_to_check_at_runtime.append("dataclasses")
if sys.version_info < (3, 8):
       pkgs_to_check_at_runtime.append("importlib_metadata")

for pkg in pkgs_to_check_at_runtime:
       if pkg in deps:
              if pkg == "tokenizers":
                     # must be loaded here, or else tqdm check may fail
                     from .utils import is_tokenizers_available

                     if not is_tokenizers_available():
                            continue  # not required, check version only if installed

              require_version_core(deps[pkg])
       else:
              raise ValueError(F"can't find {pkg} in {deps.keys()}, check dependency_versions_table.py")



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     int     ,			__SCREAMING_SNAKE_CASE							:     Union[str, Any]=None      ):
     require_version(deps[pkg]     ,			__SCREAMING_SNAKE_CASE      )

