

def 						lowerCamelCase__      ( __A    :int		):


       """simple docstring"""




       if length <= 0 or not isinstance(__A	,__A		):
              raise ValueError("""Length must be a positive integer."""		)
       return [n * (2 * n - 1) for n in range(__A		)]


if __name__ == "__main__":
    print(hexagonal_numbers(length=5))
    print(hexagonal_numbers(length=10))




def 						lowerCamelCase__      ( __A    :int	,__A    :int		):


       """simple docstring"""




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

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

       __snake_case       	=							max(len(__A		)	,len(__A		)		)

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()

