Statement

Giorgio's house has a huge bugs problem: N colonies of ants are infesting the place, and he must kill them once and for all! Since he is a very abstract person, Giorgio lives in a M-dimensional cube of side B, so that the position of every ant colony can be represented as an array of coordinates (A_1, A_2, …, A_M) with integer values ranging from 0 to B-1. Since ants are social entities, they always try to unify the colonies. Thereby, if two colonies are adjacent in the house (the position of one is obtained by adding or subtracting 1 from a single coordinate of the position of the other), they build a tunnel among them, creating a supercolony unifying the two smaller colonies and exacerbating the infestation power by orders of magnitude. Giorgio knows the positions of the N colonies, and can use pest control for destroying any one of them...