Statement

In Video Game II: Almost Video Game III, you control a character which has K abilities, numbered from 0 to K-1. The objective of this game is to defeat N bosses, which are numbered from 0 to N-1, in the order you have to beat them. At the beginning of a playthrough, none of the K abilities has been researched yet. Before facing each boss, you can research a (possibly empty) subset of the K abilities. Once an ability is researched, it will stay available for the rest of the playthrough and you do not have to research it again. After beating all bosses, the score of the playthrough is equal to b^2, where b is the number of bosses where your character had all K abilities researched. Let's consider the following playthrough for N=4 and K=3: (1) Before fighting boss 0, you research ability 2. (2) You fight boss 0 with 1 ability researched. (3) Before fighting boss 1, you don't research any new abilities. (4) You fight boss 1 with 1 ability (ability 2) researched...