Satisfying Gourmets

Remy, a chef, is preparing a dish for a group of food reviewers. The dish requires $n$ ingredients, but Remy knows that these reviewers are picky, and a bad review could cost him his career. In specific, for each ingredient, Remy has two brands of that particular ingredient, and he knows that the reviewers dislike $k$ pairs of brands from different ingredients being put together in the same dish.