





'''simple docstring'''






from copy import deepcopy




class 					UpperCAmelCase	:




      def __init__(     self     :					Optional[int]     ,     __snake_case     :					list[int] | None = None     ,     __snake_case     :					int | None = None    )							-> None:

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




      def 							lowercase__       (     self     :					int     ,     __snake_case     :					list[int]    )							-> None:
            _lowerCAmelCase					=				len(__snake_case    )
            _lowerCAmelCase					=				deepcopy(__snake_case    )
            for i in range(1     ,     self.size    ):
                  _lowerCAmelCase					=				self.next_(__snake_case    )
                  if j < self.size:
                        self.tree[j] += self.tree[i]




      def 							lowercase__       (     self     :					Optional[Any]    )							-> list[int]:
            _lowerCAmelCase					=				self.tree[:]
            for i in range(self.size - 1     ,     0     ,     -1    ):
                  _lowerCAmelCase					=				self.next_(__snake_case    )
                  if j < self.size:
                        arr[j] -= arr[i]
            return arr




      @staticmethod
      def 							lowercase__       (     __snake_case     :					int    )							-> int:
            return index + (index & (-index))




      @staticmethod
      def 							lowercase__       (     __snake_case     :					int    )							-> int:
            return index - (index & (-index))




      def 							lowercase__       (     self     :					str     ,     __snake_case     :					int     ,     __snake_case     :					int    )							-> None:
            if index == 0:
                  self.tree[0] += value
                  return
            while index < self.size:
                  self.tree[index] += value
                  _lowerCAmelCase					=				self.next_(__snake_case    )




      def 							lowercase__       (     self     :					Optional[Any]     ,     __snake_case     :					int     ,     __snake_case     :					int    )							-> None:
            self.add(__snake_case     ,     value - self.get(__snake_case    )    )




      def 							lowercase__       (     self     :					str     ,     __snake_case     :					int    )							-> int:
            if right == 0:
                  return 0
            _lowerCAmelCase					=				self.tree[0]
            right -= 1  # make right inclusive
            while right > 0:
                  result += self.tree[right]
                  _lowerCAmelCase					=				self.prev(__snake_case    )
            return result




      def 							lowercase__       (     self     :					Tuple     ,     __snake_case     :					int     ,     __snake_case     :					int    )							-> int:
            return self.prefix(__snake_case    ) - self.prefix(__snake_case    )




      def 							lowercase__       (     self     :					Optional[Any]     ,     __snake_case     :					int    )							-> int:
            return self.query(__snake_case     ,     index + 1    )




      def 							lowercase__       (     self     :					str     ,     __snake_case     :					int    )							-> int:
            value -= self.tree[0]
            if value < 0:
                  return -1

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

            _lowerCAmelCase					=				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()













'''simple docstring'''






def   UpperCamelCase__ (						lowerCAmelCase				,      lowerCAmelCase    ):





      """simple docstring"""


      _lowerCAmelCase					=				""""""
      for word_or_phrase in separated:
            if not isinstance(lowerCAmelCase				,      lowerCAmelCase    ):
                  raise Exception("""join() accepts only strings to be joined"""    )
            joined += word_or_phrase + separator
      return joined.strip(lowerCAmelCase    )


if __name__ == "__main__":
      from doctest import testmod

      testmod()






