Moovie Mooving

Bessie is at the movie theater. She wants to hide from Farmer John for the whole stretch of $L$ minutes from time $0$ to time $L$, so she has to be inside some showing at every moment of that stretch.

The theater plays $N$ movies. Movie $i$ runs for $D_i$ minutes and has a fixed list of showtimes. A showing of movie $i$ that starts at time $s$ lasts from $s$ to $s + D_i$, and Bessie may walk in late and leave early, so that showing hides her at any moment between $s$ and $s + D_i$.

Bessie never watches the same movie twice, and she cannot move to another showtime of the movie she is already watching when that showtime overlaps the one she is in. Plots confuse her when she watches too many movies, so she wants to use as few movies as she can.

Decide whether Bessie can stay inside a showing from time $0$ through time $L$. If she can, report the smallest number of movies that lets her do it.

The first line contains $N$ and $L$.

Each of the next $N$ lines describes one movie. The line starts with the duration $D$ and the number of showtimes $C$. The remaining $C$ integers on that line are the starting times of the showings of that movie. They are distinct, lie between $0$ and $L$, and are given in increasing order.

$1 \le N \le 20$, $1 \le L \le 10^8$, $1 \le D \le L$, $1 \le C \le 1000$.

Print the smallest number of movies Bessie needs to watch to stay inside a showing from time $0$ through time $L$. Print $-1$ if no choice of movies works.

In the first example Bessie sits in the first showing of the fourth movie from time $0$ to time $20$, then in the first showing of the first movie from time $20$ to time $65$, then in the last showing of the second movie from time $65$ to time $100$.