You are tasked with implementing an in-memory Task Management System. All API methods are invoked with a timestamp parameter, which represents the logical time at which the operation occurs.

Assumptions

• API calls are guaranteed to be processed in non-decreasing timestamp order.
• Task IDs and user IDs are strings (or integers).
• If an operation references a non-existent task or user, it should be a no-op (or return null/false). The chosen consistent behavior must be documented.

Data Model

Each task entity must include:

• task_id (unique identifier)
• description
• priority (integer), defaulting to 0 upon creation.
• Optional assignment to one or more users. A task can be assigned to multiple users, and each user can have multiple tasks.

Required APIs

1) CRUD Tasks

Implement the following four methods, each accepting a 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 must remove it entirely from the system and unassign 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 define).

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 specified task for deletion at logical time timestamp + delay.

Important Ordering Rule: If one or more deletions are scheduled to occur at time T, these 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 method must return the number of tasks assigned to user_id at the specified logical time time_at (where time_at <= timestamp). The result must accurately reflect all creates, deletes, assigns, unassigns, and scheduled deletions that occurred up to time_at, adhering to the same deletion-precedence rule for identical timestamps.

Constraints

You may assume the following:

• Up to approximately 200,000 operations.
• Timestamps will fit within 64-bit integers.
• Your implementation should be efficient, aiming for roughly O(log n) per operation for the most complex parts.