Raucous Rockers

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.

PROGRAM NAME: rockers

INPUT FORMAT

• Line 1: Three integers: N, T, and M.
• Line 2: N integers that are the lengths of the songs ordered by the date they were written.

SAMPLE INPUT (file rockers.in)

4 5 2
4 3 4 2

OUTPUT FORMAT

A single line with an integer that is the number of songs that will fit on M disks.

SAMPLE OUTPUT (file rockers.out)

3