





def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:Dict      ,				snake_case__	:str  )   ->    List[str]:
  _lowercase						    =			[1]
  for i in range(2      ,				snake_case__  ):
    factorials.append(factorials[-1] * i  )
  assert 0 <= k < factorials[-1] * n, "k out of bounds"

  _lowercase						    =			[]
  _lowercase						    =			list(range(snake_case__  )  )

  # Find permutation
  while factorials:
    _lowercase						    =			factorials.pop()
    _lowercase    ,		_lowercase						    =			divmod(snake_case__      ,				snake_case__  )
    permutation.append(elements[number]  )
    elements.remove(elements[number]  )
  permutation.append(elements[0]  )

  return permutation


if __name__ == "__main__":
      import doctest

      doctest.testmod()

"""simple docstring"""






from collections.abc import Callable





class 				a__					:



     def __init__(							self :Tuple      ,  _lowerCamelCase :Callable | None = None   ):







      '''simple docstring'''



      UpperCamelCase_     :					list   	=[]
      # Stores indexes of each item for supporting updates and deletion.
      UpperCamelCase_     :					dict   	={}
      # Stores current size of heap.
      UpperCamelCase_     :					Any   	=0
      # Stores function used to evaluate the score of an item on which basis ordering
      # will be done.
      UpperCamelCase_     :					List[str]   	=key or (lambda _lowerCamelCase   : x)



     def  lowerCamelCase_						(							self :Tuple      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      return int((i - 1) / 2   ) if i > 0 else None



     def  lowerCamelCase_						(							self :Optional[Any]      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					List[str]   	=int(2 * i + 1   )
      return left if 0 < left < self.size else None



     def  lowerCamelCase_						(							self :Tuple      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					Optional[Any]   	=int(2 * i + 2   )
      return right if 0 < right < self.size else None



     def  lowerCamelCase_						(							self :Dict      ,  _lowerCamelCase :int      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_	,     UpperCamelCase_     :					Optional[int]   	=(
          self.pos_map[self.arr[j][0]],
          self.pos_map[self.arr[i][0]],
      )
      # Then swap the items in the list.
      UpperCamelCase_	,     UpperCamelCase_     :					Union[str, Any]   	=self.arr[j], self.arr[i]



     def  lowerCamelCase_						(							self :Optional[Any]      ,  _lowerCamelCase :int      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      return self.arr[i][1] < self.arr[j][1]



     def  lowerCamelCase_						(							self :Any      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					int   	=self._left(_lowerCamelCase   )
      UpperCamelCase_     :					List[Any]   	=self._right(_lowerCamelCase   )
      UpperCamelCase_     :					Optional[Any]   	=i

      if left is not None and not self._cmp(_lowerCamelCase      ,  _lowerCamelCase   ):
       UpperCamelCase_     :					Optional[int]   	=left
      if right is not None and not self._cmp(_lowerCamelCase      ,  _lowerCamelCase   ):
       UpperCamelCase_     :					List[Any]   	=right

      return valid_parent



     def  lowerCamelCase_						(							self :Any      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					Dict   	=self._parent(_lowerCamelCase   )
      while parent is not None and not self._cmp(_lowerCamelCase      ,  _lowerCamelCase   ):
       self._swap(_lowerCamelCase      ,  _lowerCamelCase   )
       UpperCamelCase_	,     UpperCamelCase_     :					Dict   	=parent, self._parent(_lowerCamelCase   )



     def  lowerCamelCase_						(							self :List[str]      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					Optional[Any]   	=self._get_valid_parent(_lowerCamelCase   )
      while valid_parent != index:
       self._swap(_lowerCamelCase      ,  _lowerCamelCase   )
       UpperCamelCase_	,     UpperCamelCase_     :					int   	=valid_parent, self._get_valid_parent(_lowerCamelCase   )



     def  lowerCamelCase_						(							self :Optional[Any]      ,  _lowerCamelCase :int      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      if item not in self.pos_map:
       return
      UpperCamelCase_     :					List[Any]   	=self.pos_map[item]
      UpperCamelCase_     :					int   	=[item, self.key(_lowerCamelCase   )]
      # Make sure heap is right in both up and down direction.
      # Ideally only one of them will make any change.
      self._heapify_up(_lowerCamelCase   )
      self._heapify_down(_lowerCamelCase   )



     def  lowerCamelCase_						(							self :Tuple      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      if item not in self.pos_map:
       return
      UpperCamelCase_     :					Any   	=self.pos_map[item]
      del self.pos_map[item]
      UpperCamelCase_     :					Dict   	=self.arr[self.size - 1]
      UpperCamelCase_     :					Optional[int]   	=index
      self.size -= 1
      # Make sure heap is right in both up and down direction. Ideally only one
      # of them will make any change- so no performance loss in calling both.
      if self.size > index:
       self._heapify_up(_lowerCamelCase   )
       self._heapify_down(_lowerCamelCase   )



     def  lowerCamelCase_						(							self :Optional[int]      ,  _lowerCamelCase :int      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					Optional[int]   	=len(self.arr   )
      if arr_len == self.size:
       self.arr.append([item, self.key(_lowerCamelCase   )]   )
      else:
       UpperCamelCase_     :					str   	=[item, self.key(_lowerCamelCase   )]
      UpperCamelCase_     :					Optional[int]   	=self.size
      self.size += 1
      self._heapify_up(self.size - 1   )



     def  lowerCamelCase_						(							self :List[Any]   ):







      '''simple docstring'''



      return self.arr[0] if self.size else None




     def  lowerCamelCase_						(							self :Tuple   ):







      '''simple docstring'''



      UpperCamelCase_     :					int   	=self.get_top()
      if top_item_tuple:
       self.delete_item(top_item_tuple[0]   )
      return top_item_tuple




def       A_  (				):
 pass


if __name__ == "__main__":
 import doctest

 doctest.testmod()
