Distance from origin is sqrt(x² + y²). You never need the actual square root — compare squared distances to sort, which is faster and avoids floating-point issues.

Build a max-heap of size k: push each point's squared distance, and pop the largest when the heap exceeds k. The k points remaining in the heap are your answer.

When multiple points tie on distance, any ordering is accepted. If k equals the total number of points, return all points unchanged.