Problem D
Event Planning

You have some constraints: The total cost of the trip must be within budget, of course. All participants must stay at the same hotel, to avoid last years catastrophe, where some members got lost in the city, never being seen again.

Input

The first line of input consists of four integers: $1 \leq N \leq 200$, the number of participants, $1 \leq B \leq 500\, 000$, the budget, $1 \leq H \leq 18$, the number of hotels to consider, and $1 \leq W \leq 13$, the number of weeks you can choose between. Then follow two lines for each of the $H$ hotels. The first gives $1 \leq p \leq 10\, 000$, the price for one person staying the weekend at the hotel. The second contains $W$ integers, $0 \leq a \leq 1\, 000$, giving the number of available beds for each weekend at the hotel.

Output

Output the minimum cost of the stay for your group, or “stay home” if nothing can be found within the budget.

3 1000 2 3
200
0 2 2
300
27 3 20

900

5 2000 2 4
300
4 3 0 4
450
7 8 0 13

stay home