

def 					__lowercase      (     _A						,    _A			)     ->						str:
      if number < 0 or shift_amount < 0:
            raise ValueError("""both inputs must be positive integers"""			)

      SCREAMING_SNAKE_CASE :      int       =   str(bin(_A			)			)
      binary_number += "0" * shift_amount
      return binary_number






def 					__lowercase      (     _A						,    _A			)     ->						str:
      if number < 0 or shift_amount < 0:
            raise ValueError("""both inputs must be positive integers"""			)

      SCREAMING_SNAKE_CASE :      Union[str, Any]       =   str(bin(_A			)			)[2:]
      if shift_amount >= len(_A			):
            return "0b0"
      SCREAMING_SNAKE_CASE :      int       =   binary_number[: len(_A			) - shift_amount]
      return "0b" + shifted_binary_number






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

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()







def 					__lowercase      (     _A						,    _A			)     ->						int:
      assert x is not None
      assert y is not None

      SCREAMING_SNAKE_CASE :      int       =   len(_A			)
      SCREAMING_SNAKE_CASE :      Union[str, Any]       =   len(_A			)

      # declaring the array for storing the dp values
      SCREAMING_SNAKE_CASE :      Tuple       =   [[0] * (n + 1) for _ in range(m + 1			)]  # noqa: E741

      for i in range(1						,    m + 1			):
            for j in range(1						,    n + 1			):
                  SCREAMING_SNAKE_CASE :      List[Any]       =   1 if x[i - 1] == y[j - 1] else 0

                  SCREAMING_SNAKE_CASE :      int       =   max(l[i - 1][j]						,    l[i][j - 1]						,    l[i - 1][j - 1] + match			)

      SCREAMING_SNAKE_CASE :      int       =   """"""
      SCREAMING_SNAKE_CASE     ,	SCREAMING_SNAKE_CASE :      int       =   m, n
      while i > 0 and j > 0:
            SCREAMING_SNAKE_CASE :      Tuple       =   1 if x[i - 1] == y[j - 1] else 0

            if l[i][j] == l[i - 1][j - 1] + match:
                  if match == 1:
                        SCREAMING_SNAKE_CASE :      List[Any]       =   x[i - 1] + seq
                  i -= 1
                  j -= 1
            elif l[i][j] == l[i - 1][j]:
                  i -= 1
            else:
                  j -= 1

      return l[m][n], seq


if __name__ == "__main__":
  UpperCAmelCase__ :     str				    =    """AGGTAB"""
  UpperCAmelCase__ :     Optional[int]				    =    """GXTXAYB"""
  UpperCAmelCase__ :     Tuple				    =    4
  UpperCAmelCase__ :     Dict				    =    """GTAB"""

  UpperCAmelCase__    ,   UpperCAmelCase__ :     Optional[int]				    =    longest_common_subsequence(a, b)
  print("""len =""", ln, """, sub-sequence =""", subseq)
  import doctest

  doctest.testmod()




