Produce a Deterministic Course Plan

There are num_courses courses numbered 0 through num_courses - 1. Each prerequisite pair is [course, prerequisite], meaning prerequisite must appear before course.

def prerequisite_plan(
 num_courses: int,
 prerequisites: list[list[int]]
) -> list[object]:
 ...

Return [true, order] if every course can be completed, where order is the lexicographically smallest valid list of all course IDs. Return [false, []] if the requirements contain a cycle. Duplicate prerequisite pairs do not change the result.

Constraints and Boundary Rules

• 0 <= num_courses <= 200000
• 0 <= len(prerequisites) <= 400000
• Every pair must contain exactly two integer IDs in range.
• Self-dependencies are cycles.
• For num_courses == 0, return [true, []].
• Malformed pairs or out-of-range IDs must raise ValueError.
• Inputs and outputs are JSON-marshalable and outputs are compared exactly.

Examples

Input: num_courses = 4
 prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2]]
Output: [true, [0, 1, 2, 3]]

Input: num_courses = 2
 prerequisites = [[1, 0], [0, 1]]
Output: [false, []]

Input: num_courses = 3
 prerequisites = []
Output: [true, [0, 1, 2]]

Hints

• Model what makes a course eligible at any moment.
• The ordinary valid-order problem does not choose between simultaneous options; the requested output does.
• Ensure duplicate edges do not distort eligibility.