IOI 2016 Aliens - Problem Statement

A satellite photographs $n$ points on an $m \times m$ grid using square photos taken along the diagonal. Use at most $k$ photos to cover all points, reducing total cells photographed (overlapping cells count multiple times).

This problem gives the technique its name. It combines Aliens Trick with Convex Hull Trick for full improvement. The structure: partition points into groups, each covered by one photo. Exactly $k$ groups (at most $k$ photos). Find the lowest area with overlap penalties.