The economy has been pretty bad lately, and it's affecting the village in north pole too...

This year, Santa is afraid not everyone can get a toy on their wishlist. To check if this is the case, Santa uses a small sample of ~N~ children's wishlists and wants to know how many of them can have at least one item fulfilled in their wishlist with an optimal distribution of toys.

There are ~M~ different toys that children have put on their wishlist this year. Santa estimates that with his proportion of the sample to real-life population, he currently has enough resources to make ~a_i~ units of the ~i~-th toy.

Each child has put ~C_i~ toys on their wishlist, each a distinct toy between ~1~ and ~M~ inclusive.

Santa wants to know the percent of children that can recieve a toy from their wishlist based on his sample. Can you help him?

Constraints

For all subtasks,

~1 \le N, M, a_i \le 300~

~1 \le C_i \le M~

Subtask 1 [20%]

~1 \le N, M \le 10~

~a_i = 1~

Subtask 2 [30%]

~a_i = 1~

Subtask 3 [50%]

No additional constraints.

Input Specification

The first line of input will contain ~2~ space-separated integers ~N~ and ~M~.

The next ~N~ lines will first contain ~C_i~, followed by a space, followed by ~C_i~ distinct space-separated integers between ~1~ and ~M~, denoting the wishlist for the ~i~-th child.

The final line will contain ~M~ space-separated integers ~a_i~.

Output Specification

Output a number ~X \ (0 \le X \le 100)~, the percent of children that can recieve a toy from their wishlist in this sample. Outputs with a relative or absolute error of ~10^{-4}~ will be accepted.

Sample Input 1

3 2
2 1 2
1 1
1 1
1 2

Sample Output 1

66.6666

Explanation for Sample Output 1

All ~3~ children want toy ~1~ and only child ~1~ wants both toys ~1~ and ~2~. We can give child ~1~ toy ~2~, but since there is only one of toy ~1~, We can give either child ~2~ or ~3~ toy ~1~ but not both.

Thus, a maximum of ~\frac{2}{3} = 66.6666 \%~ of children can recieve a toy from their wishlist.

Sample Input 2

5 5
2 1 4
2 3 1
1 1
3 2 3 1
1 4
2 1 1 2 100

Sample Output 2

100.0000

Explanation for Sample Output 2

If we give one of toy ~1~ to child ~3~, one of toy ~2~ to child ~4~, one of toy ~3~ to child ~2~, and one of toy ~4~ each to child ~1~ and ~5~, everyone can recieve a toy, so ~100 \%~ of children can get toys from their wishlist.