The highest-level Pokémon of each type ~1 \dots K~ should certainly be chosen. In addition to those ~K~ Pokémon, the ~M-K~ highest-level Pokémon of the remaining ~N-K~ ones should also be chosen to round out the team. We can refer to these additional ~M-K~ Pokémon as "extras".

Let's sort all ~N~ Pokémon in non-increasing order of level, such that the highest-level ones come first, and then iterate over them in that order while greedily determining which ones to choose. Along the way, we'll maintain several pieces of information: the level sum of Pokémon chosen so far, an array indicating whether or not we've already chosen a Pokémon of type ~t~ (for each possible ~t~), and the number of extras chosen so far.

When considering the ~i~-th Pokémon, if we have not yet chosen a Pokémon of type ~T_i~, then we should go ahead and choose this one, as it must be the highest-level Pokémon of its type. Otherwise, if we have not yet chosen ~M-K~ extras, then we should go ahead and choose this one as an extra, as it must be the highest-level valid extra.

Upon processing all ~N~ Pokémon in this manner, we're guaranteed to have successfully chosen the highest-level one of each type as well as the ~M-K~ highest-level valid extras, meaning that our aggregated sum of chosen Pokémon levels must be optimal. The time complexity of this solution is ~\mathcal O(N \log N)~, necessary for sorting the Pokémon.