Lighting Rectangle

You are given an axis-aligned rectangle in a 2D Cartesian plane. The bottom left corner of this rectangle has coordinates $(0, 0)$ and the top right corner has coordinates $(N-1, N-1)$. You are also given $K$ light sources; each light source is a point inside or on the perimeter of the rectangle. For each light source, let's divide the plane into four quadrants by a horizontal and a vertical line