Statement

William is attending the finals of Master Chef Italia! For this last round of selection he will have to prepare N different dishes, each of them taking H_i units of heat in order to be cooked. Time is very limited, so he needs to plan carefully in order to cook everything in time. For this round, William will be provided of M stoves of various sizes, each of them taking T_i seconds to emit a full unit of heat (larger stoves are faster, smaller ones are slower). On each stove, William can put only one of the dishes he has to prepare at a time: he may put other ones only after the dishes previously cooked there are ready. Furthermore, each dish can only be put on a single stove from the beginning until the end: changing stoves halfway through cooking may seriously impair the quality of the prepared dishes. After spending half of his time planning, William is still puzzled about how to schedule the different dishes on the various stoves...