





def 					__SCREAMING_SNAKE_CASE  (							__lowercase:		List[Any]     ,							__lowercase:		List[str]):



  '''simple docstring'''






  __lowerCAmelCase			=				1
  while b > 0:
    if b & 1:
      res *= a

    a *= a
    b >>= 1

  return res


def 					__SCREAMING_SNAKE_CASE  (							__lowercase:		List[str]     ,							__lowercase:		int     ,							__lowercase:		Union[str, Any]):



  '''simple docstring'''






  __lowerCAmelCase			=				1
  while b > 0:
    if b & 1:
      __lowerCAmelCase			=				((res % c) * (a % c)) % c

    a *= a
    b >>= 1

  return res







class   __snake_case				:






    '''simple docstring'''





    def __init__(   self						:		Any							):

      """simple docstring"""





      __lowerCAmelCase			=				{}
      # indexmap keys are an index and it's values are the number at that index
      __lowerCAmelCase			=				{}





    def 	A		(   self						:		List[Any]			,						snake_case						:		list | str | range			,						snake_case						:		int							):

      """simple docstring"""





      if isinstance(snake_case			,						(range, str)							):
        __lowerCAmelCase			=				list(snake_case							)
      elif not isinstance(snake_case			,						snake_case							):
        raise TypeError(
            '''binary_search_delete() only accepts either a list, range or str'''							)

      __lowerCAmelCase			=				0
      __lowerCAmelCase			=				len(snake_case							) - 1

      while low <= high:
        __lowerCAmelCase			=				(low + high) // 2
        if array[mid] == item:
          array.pop(snake_case							)
          return array
        elif array[mid] < item:
          __lowerCAmelCase			=				mid + 1
        else:
          __lowerCAmelCase			=				mid - 1
      raise ValueError(
          '''Either the item is not in the array or the array was unsorted'''							)





    def 	A		(   self						:		Tuple			,						snake_case						:		list | str | range			,						snake_case						:		int							):

      """simple docstring"""





      if isinstance(snake_case			,						(range, str)							):
        __lowerCAmelCase			=				list(snake_case							)
      elif not isinstance(snake_case			,						snake_case							):
        raise TypeError(
            '''binary_search_insert() only accepts either a list, range or str'''							)

      __lowerCAmelCase			=				0
      __lowerCAmelCase			=				len(snake_case							) - 1

      while low <= high:
        __lowerCAmelCase			=				(low + high) // 2
        if array[mid] == index:
          # If the item already exists in the array,
          # insert it after the existing item
          array.insert(mid + 1			,						snake_case							)
          return array
        elif array[mid] < index:
          __lowerCAmelCase			=				mid + 1
        else:
          __lowerCAmelCase			=				mid - 1

        # If the item doesn't exist in the array, insert it at the appropriate position
      array.insert(snake_case			,						snake_case							)
      return array





    def 	A		(   self						:		Tuple			,						snake_case						:		int			,						snake_case						:		int							):

      """simple docstring"""





      if index in self.indexmap:
        __lowerCAmelCase			=				self.indexmap[index]
        if len(self.numbermap[n]							) == 1:
          del self.numbermap[n]
        else:
          __lowerCAmelCase			=				self.binary_search_delete(self.numbermap[n]			,						snake_case							)

        # Set new index
      __lowerCAmelCase			=				number

      # Number not seen before or empty so insert number value
      if number not in self.numbermap:
        __lowerCAmelCase			=				[index]

      # Here we need to perform a binary search insertion in order to insert
      # The item in the correct place
      else:
        __lowerCAmelCase			=				self.binary_search_insert(
            self.numbermap[number]			,						snake_case							)





    def 	A		(   self						:		List[str]			,						snake_case						:		int							):

      """simple docstring"""





      return self.numbermap.get(snake_case			,						[-1]							)[0]


if __name__ == "__main__":
      import doctest

      doctest.testmod()
