Design a Lottery System with O(1) Delete

Problem Design a lottery system maintaining a dynamic set S (elements can be integers or strings) supporting: add(x): if x is not in the set, add it and return true; otherwise return false. remove(x): if x is in the set, remove it and return true; otherwise return false. draw(): return a uniformly random element from the current set. Requirements: The expected time complexity of all three operations must be O(1). Provide the data structure design and key implementation details. Example Input add 1 add 2 add 1 draw remove 2 remove 3 draw Output true true false (1 or 2) true false 1