Problem

In a Meta-style ranking or retrieval pipeline, you may need to quickly keep only the nearest candidate embeddings or coordinates. Given a list of points on a 2D plane, return the k points closest to the origin (0, 0).

The distance between a point (x, y) and the origin is sqrt(x^2 + y^2). For efficiency, compare points using squared distance x^2 + y^2 instead of computing square roots. You may return the answer in any order.

Formal Specification

• Input:
  • points: a list of 2-element lists, where each element is [x, y]
  • k: an integer
• Output:
  • A list containing exactly k points from points with the smallest distances to the origin

Examples

Example 1

• Input: points = [[1,3],[-2,2]], k = 1
• Output: [[-2,2]]
• Explanation: Squared distances are 10 and 8, so [-2,2] is closer.

Example 2

• Input: points = [[3,3],[5,-1],[-2,4]], k = 2
• Output: [[3,3],[-2,4]]
• Explanation: Squared distances are 18, 26, and 20. The two smallest are 18 and 20.

Constraints

• 1 <= len(points) <= 10^4
• -10^4 <= x, y <= 10^4
• 1 <= k <= len(points)
• Each point is represented as exactly two integers