





def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=[0 for i in range(r + 1  )]
   # nc0 = 1
   UpperCAmelCase_											=1
   for i in range(1  ,    n + 1  ):
      # to compute current row from previous row.
      UpperCAmelCase_											=min(lowercase__  ,    lowercase__  )
      while j > 0:
         c[j] += c[j - 1]
         j -= 1
   return c[r]





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











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

__lowercase  :   Optional[int]						      ="""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     a__ (					lowercase__  ,    lowercase__=None  ):






   '''simple docstring'''






   require_version(deps[pkg]  ,    lowercase__  )




