Choose K pickup locations minimizing L1 distance

## Coding: K Shuttle Pickup Locations (L1) You are given the coordinates of **N people** on a 2D grid. You want to open **K shuttle pickup locations** (pickup points) so that the **sum of Manhattan (L1) distances** from each person to their **nearest** pickup location is minimized. ### Input - An integer `N` (number of people). - An array `points` of length `N`, where `points[i] = (xi, yi)` are integer coordinates. - An integer `K` (number of pickup locations). ### Output - Return the **minimum possible total L1 distance**: \[ \sum_{i=1}^{N} \min_{j=1..K} (|x_i - X_j| + |y_i - Y_j|) \] where \((X_j, Y_j)\) are the chosen pickup locations. ### Clarifications / assumptions (state in your solution) - Are pickup locations required to be at integer coordinates? - Are pickup locations required to be chosen from existing people’s coordinates, or can they be anywhere? ### Constraints (you may assume) Provide an algorithm appropriate for interview constraints (e.g., `N` up to a few thousand, `K` up to `N`).