Problem Statement

When Yuki streams live, she plays songs by a group called Clararis as background music.
Yuki's music player has $N$ songs by Clararis registered, and the length of the $k$-th song is $S_k$.
Yuki's live stream lasts $L$ minutes.
The music player has a shuffle feature: first, the registered songs are randomly reordered and then played in that order.
After all the songs have been played, they are randomly reordered again and played in that order.
Write a program that computes the expected number of songs that play for at least $1$ second during Yuki's stream.
For each random reordering, assume that all $N!$ possible orderings are equally likely, and that each reordering is done independently.
Yuki starts playback at the same moment the live stream begins.

Input

$N$ $L$
$S_1$ $S_2$ $\cdots$ $S_N$

$1 \leq N \leq 50$
$1 \leq L \leq 300$
$S_k$ is a string of the form $\verb|MM:SS|$, indicating that the length of the song is $\verb|MM|$ minutes and $\verb|SS|$ seconds ($00 \leq \verb|MM|,\verb|SS| \leq 59$, and $\verb|MM:SS| \neq 00\verb|:|00$)

Output

Output the expected number of songs played during the live stream on $1$ line.
Your answer is considered correct if the relative error is at most $10^{-9}$.
Print a newline at the end.

Sample

5 30
10:30 20:47 08:14 29:59 05:24

2.6

2 1
00:59 01:00

1.5

4 300
00:01 00:02 00:01 00:03

4