# Return the K Closest Points with Deterministic Ties Implement `k_closest(points, target, k)`. Each point and the target are integer pairs. Return exactly `k` input points with smallest squared Euclidean distance to the target, ordered by `(distance, x, y, original_index)` so ties have one canonical result. Constraints: `0 <= k <= len(points) <= 200000`; coordinates are integers between `-10^6` and `10^6`, so every squared distance is at most `8 * 10^12` and is exact in all four languages. Do not use square roots. Aim for `O(n log k)` time and `O(k)` auxiliary space. ```hint Make ties observable Include duplicate coordinates and different points at equal distance so the required ordering is exercised. ```