





def      A__       (    SCREAMING_SNAKE_CASE_   :      str				,	SCREAMING_SNAKE_CASE_   :      Tuple						)  ->  List[Any]:






   """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(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))






def      A__       (    SCREAMING_SNAKE_CASE_   :      int				,	SCREAMING_SNAKE_CASE_   :      int						)  ->  str:






   """simple docstring"""







   if a < 0 or b < 0:
      raise ValueError('''the value of both inputs must be positive'''						)

   _UpperCAmelCase           =   str(bin(SCREAMING_SNAKE_CASE_						)						)[2:]  # remove the leading "0b"
   _UpperCAmelCase           =   str(bin(SCREAMING_SNAKE_CASE_						)						)[2:]  # remove the leading "0b"

   _UpperCAmelCase           =   max(len(SCREAMING_SNAKE_CASE_						)				,	len(SCREAMING_SNAKE_CASE_						)						)

   return "0b" + "".join(
       str(int(char_a == '''1''' and char_b == '''1'''						)						)
       for char_a, char_b in zip(a_binary.zfill(SCREAMING_SNAKE_CASE_						)				,	b_binary.zfill(SCREAMING_SNAKE_CASE_						)						)						)


if __name__ == "__main__":
   import doctest

   doctest.testmod()