A1029.Bessies Birthday Buffet

For Bessie the cow鈥檚 birthday, Farmer John has given her free reign over one
of his best fields to eat grass.
The field is covered in $N$ patches of grass ($1 \le N \le 1000$),
conveniently numbered $1\ldots N$, that each have a distinct quality value. If
Bessie eats grass of quality $Q$, she gains $Q$ units of energy. Each patch is
connected to up to 10 neighboring patches via bi-directional paths, and it
takes Bessie $E$ units of energy to move between adjacent patches ($1 \le E \le 1,000,000$). Bessie can choose to start grazing in any patch she wishes,
and she wants to stop grazing once she has accumulated a maximum amount of
energy.
Unfortunately, Bessie is a picky bovine, and once she eats grass of a certain
quality, she鈥檒l never eat grass at or below that quality level again! She is
still happy to walk through patches without eating their grass; in fact, she
might find it beneficial to walk through a patch of high-quality grass without
eating it, only to return later for a tasty snack.
Please help determine the maximum amount of energy Bessie can accumulate.

The first line of input contains $N$ and $E$. Each of the remaining $N$ lines
describe a patch of grass. They contain two integers $Q$ and $D$ giving the
quality of the patch (in the range $1\ldots 1,000,000$) and its number of
neighbors. The remaining $D$ numbers on the line specify the neighbors.

Please output the maximum amount of energy Bessie can accumulate.

Bessie starts at patch 4 gaining 5 units of energy from the grass there. She
then takes the path to patch 5 losing 2 units of energy during her travel. She
refuses to eat the lower quality grass at patch 5 and travels to patch 3 again
losing 2 units of energy. Finally she eats the grass at patch 3 gaining 6
units of energy for a total of 7 energy.
Note tha the sample case above is different from test case 1 when you submit.