





'''simple docstring'''




def 			_lowerCAmelCase     (    __snake_case    :					int					,				__snake_case    :					int     )	->	str:
     if number < 0 or shift_amount < 0:
          raise ValueError('both inputs must be positive integers'     )

     __A		:					Optional[Any]						=			str(bin(__snake_case     )     )
     binary_number += "0" * shift_amount
     return binary_number






def 			_lowerCAmelCase     (    __snake_case    :					int					,				__snake_case    :					int     )	->	str:
     if number < 0 or shift_amount < 0:
          raise ValueError('both inputs must be positive integers'     )

     __A		:					List[str]						=			str(bin(__snake_case     )     )[2:]
     if shift_amount >= len(__snake_case     ):
          return "0b0"
     __A		:					Any						=			binary_number[: len(__snake_case     ) - shift_amount]
     return "0b" + shifted_binary_number






def 			_lowerCAmelCase     (    __snake_case    :					int					,				__snake_case    :					int     )	->	str:
     if number >= 0:  # Get binary representation of positive number
          __A		:					Optional[Any]						=			'0' + str(bin(__snake_case     )     ).strip('-'     )[2:]
     else:  # Get binary (2's complement) representation of negative number
          __A		:					Union[str, Any]						=			len(bin(__snake_case     )[3:]     )  # Find 2's complement of number
          __A		:					Any						=			bin(abs(__snake_case     ) - (1 << binary_number_length)     )[3:]
          __A		:					Optional[Any]						=			(
              '1' + '0' * (binary_number_length - len(__snake_case     )) + binary_number
          )

     if shift_amount >= len(__snake_case     ):
          return "0b" + binary_number[0] * len(__snake_case     )
     return (
         "0b"
         + binary_number[0] * shift_amount
         + binary_number[: len(__snake_case     ) - shift_amount]
     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()






'''simple docstring'''




def 			_lowerCAmelCase     (    __snake_case    :					int					,				__snake_case    :					int					,				__snake_case    :					int     )	->	float:
     __A		:					Dict						=			(num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
     # formula for sum of series
     return total






def 			_lowerCAmelCase     (    )	->	Union[str, Any]:
     print(sum_of_series(1					,				1					,				10     )     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()