Statement

William just got an aggressive form of the seasonal flu, and the doctor prescribed him a broad-spectrum antibiotic to fight it, the Panaceaxyl^. This antibiotic has to be assumed in a strictly controlled pattern, exactly once every T hours, until the flu is defeated: never stop a treatment early, or the illness will get much worse! Even the slightest transgression to the prescription, such as anticipating the timing by just a few minutes, might result in one of the numerous Panaceaxyl^ side effects. However, William is a very busy person, having already taken N commitments on his agenda, each on a different hour H_i. It would not be a good idea to plan the antibiotic for one of these hours: William is definitely going to forget about it if he is distracted by other business! More precisely, if William is going to start the treatment in hour X, he needs to have hours: X, X+T, X+2T, …, X+iT, … free from commitments for all i>0...