K Closest Points to Origin

Given n points on a plane, print the k points closest to the origin (0, 0) (Euclidean distance).

Input:

• line 1: n k
• next n lines: x y

Output: k lines x y, ordered by distance (closest first). Break ties by smaller x, then smaller y. (Points may repeat; print repeats separately.)

Constraints: 1 ≤ k ≤ n ≤ 5·10⁴, −10⁴ ≤ x, y ≤ 10⁴.

Think about it: compare squared distances x² + y² — no square roots, no floating-point errors (they fit in 32-bit ints). A max-heap of size k keeps the best k seen so far in O(n log k).