The lovely WrongAnswer is very fond of independent set problems. For his thesis defense in CTSC2017, he prepared a paper on independent sets.
One day, WrongAnswer decided he would use this paper to set a question. The question he eventually came up with was:
Subtasks #  Score  Constraints 

1  6  \(1 \leq n \leq 20\) 
2  17  \(1 \leq n \leq 2000\) \(1 \leq k \leq 10000\) 
3  21  \(1 \leq n \leq 2000\) 
4  27  The tree is a line; every vertex has degree at most 2. 
5  29  No additional constraints 
The first line contains one integer \(n\).
The second line contains one integer \(k\).
The third line contains \(n  1\) integers, the \(i^{th}\) of which represents the first endpoint of the \(i^{th}\) edge (vertices 0indexed).
The fourth line contains \(n  1\) integers, the \(i^{th}\) of which represents the second endpoint of the \(i^{th}\) edge.
The fifth line contains one integer \(I\), the size of \(I\).
The sixth line contains \(I\) integers \(I_1, I_2, \ldots, I_{I}\), representing the elements of \(I\). It is guaranteed that \(I\) is a valid independent set.
Let your answer be the independent set \(S\) (If there is no valid \(S\), let \(S = \emptyset\)). Output one line containing \(S\) integers, the elements of \(S\) in ascending order.
Sample Input 1  Sample Output 1 
10
4

6 7 9

Subtask  Score 

1  6 
2  17 
3  21 
4  27 
5  29 
6  0 