You just inherited the rights to N (1 <= N <= 20) previously unreleased songs recorded by the popular group Raucous Rockers. You plan to release a set of M (1 <= M <= 20) compact disks with a selection of these songs. Each disk can hold a maximum of T (1 <= T <= 20) minutes of music, and a song can not overlap from one disk to another.
Since you are a classical music fan and have no way to judge the artistic merits of these songs, you decide on the following criteria for making the selection:
- The songs on the set of disks must appear in the order of the dates that they were written.
- The total number of songs included will be maximized.