Implement timestamped task management system APIs

You are implementing an in-memory **Task Management System**. All API methods are called with a `timestamp` representing the logical time when the operation happens. Assume: - API calls are processed in **non-decreasing `timestamp` order**. - Task IDs and user IDs are strings (or ints). - If an operation references a non-existent task/user, it should be a no-op (or return null/false) — choose a consistent behavior and document it. ## Data model Each task has: - `task_id` - `description` - `priority` (integer), default `0` at creation - optional assignment to one or more users (define whether multiple users can be assigned; if unspecified, assume **a task can be assigned to multiple users** and each user can have multiple tasks) ## Required APIs ### 1) CRUD tasks Implement four methods (all take `timestamp`): - `createTask(timestamp, task_id, description)` - `getTask(timestamp, task_id) -> description | null` - `updateTask(timestamp, task_id, new_description)` - `deleteTask(timestamp, task_id)` Deleting a task removes it from the system and unassigns it from all users. ### 2) Priorities and sorted retrieval Implement: - `updateTaskPriority(timestamp, task_id, new_priority)` - `getSortedPrioritizedTasks(timestamp) -> List[task_id]` `getSortedPrioritizedTasks` should return all **currently existing** tasks sorted by: 1. higher `priority` first 2. tie-break by `task_id` ascending (or another deterministic rule you state) ### 3) Users, assignment, and scheduled deletion Implement: - `addUser(timestamp, user_id)` - `assignTaskToUser(timestamp, user_id, task_id)` - `unassignTaskToUser(timestamp, user_id, task_id)` - `scheduleDeletion(timestamp, task_id, delay)` `scheduleDeletion` schedules the task to be deleted at time `timestamp + delay`. **Important ordering rule:** If one or more deletions are scheduled to occur at time `T`, then at timestamp `T` those deletions must be applied **before any other operations at the same timestamp `T`**. ### 4) Time-travel query Implement: - `getUserTaskNumsAt(timestamp, user_id, time_at) -> int` This returns the number of tasks assigned to `user_id` **at logical time `time_at`** (where `time_at <= timestamp`). The result must reflect all creates/deletes/assigns/unassigns/scheduled-deletes that happened up to `time_at`, with the same deletion-precedence rule at identical timestamps. ## Constraints (you may assume) - Up to ~200k operations. - Timestamps fit in 64-bit integers. - Your implementation should be efficient (roughly near O(log n) per operation for the expensive parts).