



from copy import deepcopy

class   _A   :


      '''simple docstring'''





      def __init__(	self	:							List[Any]							,      lowerCamelCase	:							Optional[Any] = None							,      lowerCamelCase	:							Dict = None	):






       '''simple docstring'''



       if arr is None and size is not None:
        __lowercase		       =			size
        __lowercase		       =			[0] * size
       elif arr is not None:
        self.init(lowerCamelCase	)
       else:
        raise ValueError("Either arr or size must be specified"	)



      def     _snake_case	(	self	:							Optional[int]							,      lowerCamelCase	:							Optional[int]	):






       '''simple docstring'''



       __lowercase		       =			len(lowerCamelCase	)
       __lowercase		       =			deepcopy(lowerCamelCase	)
       for i in range(1							,      self.size	):
        __lowercase		       =			self.next_(lowerCamelCase	)
        if j < self.size:
         self.tree[j] += self.tree[i]



      def     _snake_case	(	self	:							Tuple	):






       '''simple docstring'''



       __lowercase		       =			self.tree[:]
       for i in range(self.size - 1							,      0							,      -1	):
        __lowercase		       =			self.next_(lowerCamelCase	)
        if j < self.size:
         arr[j] -= arr[i]
       return arr



      @staticmethod
      def     _snake_case	(	lowerCamelCase	:							List[Any]	):






       '''simple docstring'''



       return index + (index & (-index))



      @staticmethod
      def     _snake_case	(	lowerCamelCase	:							Tuple	):






       '''simple docstring'''



       return index - (index & (-index))



      def     _snake_case	(	self	:							Optional[int]							,      lowerCamelCase	:							Tuple							,      lowerCamelCase	:							str	):






       '''simple docstring'''



       if index == 0:
        self.tree[0] += value
        return
       while index < self.size:
        self.tree[index] += value
        __lowercase		       =			self.next_(lowerCamelCase	)



      def     _snake_case	(	self	:							List[str]							,      lowerCamelCase	:							Optional[int]							,      lowerCamelCase	:							Tuple	):






       '''simple docstring'''



       self.add(lowerCamelCase							,      value - self.get(lowerCamelCase	)	)



      def     _snake_case	(	self	:							int							,      lowerCamelCase	:							Optional[Any]	):






       '''simple docstring'''



       if right == 0:
        return 0
       __lowercase		       =			self.tree[0]
       right -= 1  # make right inclusive
       while right > 0:
        result += self.tree[right]
        __lowercase		       =			self.prev(lowerCamelCase	)
       return result



      def     _snake_case	(	self	:							Tuple							,      lowerCamelCase	:							Any							,      lowerCamelCase	:							int	):






       '''simple docstring'''



       return self.prefix(lowerCamelCase	) - self.prefix(lowerCamelCase	)



      def     _snake_case	(	self	:							int							,      lowerCamelCase	:							List[Any]	):






       '''simple docstring'''



       return self.query(lowerCamelCase							,      index + 1	)



      def     _snake_case	(	self	:							int							,      lowerCamelCase	:							Any	):






       '''simple docstring'''



       value -= self.tree[0]
       if value < 0:
        return -1

       __lowercase		       =			1  # Largest power of 2 <= size
       while j * 2 < self.size:
        j *= 2

       __lowercase		       =			0

       while j > 0:
        if i + j < self.size and self.tree[i + j] <= value:
         value -= self.tree[i + j]
         i += j
        j //= 2
       return i


if __name__ == "__main__":
 import doctest

 doctest.testmod()








def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	# bit count represents no. of bits in the gray code
	if bit_count < 0:
		raise ValueError("The given input must be positive"   )

	# get the generated string sequence
	__lowercase		       =			gray_code_sequence_string(_SCREAMING_SNAKE_CASE   )
	#
	# convert them to integers
	for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
		__lowercase		       =			int(sequence[i]  ,	2   )

	return sequence



def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	# The approach is a recursive one
	# Base case achieved when either n = 0 or n=1
	if bit_count == 0:
		return ["0"]

	if bit_count == 1:
		return ["0", "1"]

	__lowercase		       =			1 << bit_count  # defines the length of the sequence
	# 1<< n is equivalent to 2^n

	# recursive answer will generate answer for n-1 bits
	__lowercase		       =			gray_code_sequence_string(bit_count - 1   )

	__lowercase		       =			[]

	# append 0 to first half of the smaller sequence generated
	for i in range(seq_len // 2   ):
		__lowercase		       =			"0" + smaller_sequence[i]
		sequence.append(_SCREAMING_SNAKE_CASE   )

	# append 1 to second half ... start from the end of the list
	for i in reversed(range(seq_len // 2   )   ):
		__lowercase		       =			"1" + smaller_sequence[i]
		sequence.append(_SCREAMING_SNAKE_CASE   )

	return sequence


if __name__ == "__main__":
	import doctest

	doctest.testmod()



