K Closest Points to Origin (N log K)

Given a 2D integer array points where points[i] = [xi, yi] represents a point on the plane, and an integer K, return the K points closest to the origin (0,0) (Euclidean distance). Requirements: Your solution must run in O(N log K) time. If multiple points have the same distance, any order is acceptable. Input (stdin) Line 1: integer N (number of points) Next N lines: two integers xi yi Last line: integer K Output (stdout) Print K lines, each as xi yi. Constraints 1 <= K <= N <= 2 * 10^5 -10^4 <= xi, yi <= 10^4 Example Input: 5 1 3 -2 2 5 8 0 1 -1 -1 2 One valid output: -2 2 0 1 Example Input 5 1 3 -2 2 5 8 0 1 -1 -1 2 Output -2 2 0 1