Minimum delivery factor

A render farm runs one batch a night on a single machine and never idles between jobs. Job i was submitted at minute submitted_at[i] and needs render_minutes[i] of machine time, always at least one minute. The batch begins at minute start_at, by which point every job is queued. The contract promises each customer delivery by their own submission minute plus factor times their own render minutes, so a heavy job is allowed proportionally more room than a light one. The farm may run the batch in whatever order it likes. Return the smallest whole factor for which some order delivers every job on time, and 0 for an empty batch. Note that the promised times, and therefore the order they suggest, move as the factor moves.