






"""simple docstring"""





# This is the module that test_patching.py uses to test patch_submodule()

import os  # noqa: this is just for tests
import os as renamed_os  # noqa: this is just for tests
from os import path  # noqa: this is just for tests
from os import path as renamed_path  # noqa: this is just for tests
from os.path import join  # noqa: this is just for tests
from os.path import join as renamed_join  # noqa: this is just for tests


A__					: Dict=	open  # noqa: we just need to have a builtin inside this module to test it properly












"""simple docstring"""





from copy import deepcopy
class    __lowerCamelCase    :

   def __init__(					self ,				snake_case_ = None ,				snake_case_ = None      )		->       None:

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

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_      )		->       None:
       UpperCamelCase__         =    len(snake_case_      )
       UpperCamelCase__         =    deepcopy(snake_case_      )
       for i in range(1 ,				self.size      ):
           UpperCamelCase__         =    self.next_(snake_case_      )
           if j < self.size:
               self.tree[j] += self.tree[i]

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       list[int]:
       UpperCamelCase__         =    self.tree[:]
       for i in range(self.size - 1 ,				0 ,				-1      ):
           UpperCamelCase__         =    self.next_(snake_case_      )
           if j < self.size:
               arr[j] -= arr[i]
       return arr

   @staticmethod
   def 						SCREAMING_SNAKE_CASE__ (					snake_case_      )		->       int:
       return index + (index & (-index))

   @staticmethod
   def 						SCREAMING_SNAKE_CASE__ (					snake_case_      )		->       int:
       return index - (index & (-index))

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       None:
       if index == 0:
           self.tree[0] += value
           return
       while index < self.size:
           self.tree[index] += value
           UpperCamelCase__         =    self.next_(snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       None:
       self.add(snake_case_ ,				value - self.get(snake_case_      )      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_      )		->       int:
       if right == 0:
           return 0
       UpperCamelCase__         =    self.tree[0]
       right -= 1  # make right inclusive
       while right > 0:
           result += self.tree[right]
           UpperCamelCase__         =    self.prev(snake_case_      )
       return result

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       int:
       return self.prefix(snake_case_      ) - self.prefix(snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_      )		->       int:
       return self.query(snake_case_ ,				index + 1      )







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

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

       UpperCamelCase__         =    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()




