Cow and Vacation

Description:

Input:

The first line contains three integers $$$n$$$, $$$k$$$, and $$$r$$$ ($$$2 \le n \le 2 \cdot 10^5$$$, $$$1 \le k,r \le n$$$)  — the number of cities, the maximum number of roads Bessie is willing to travel through in a row without resting, and the number of rest stops.

Each of the following $$$n-1$$$ lines contain two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i, y_i \le n$$$, $$$x_i \neq y_i$$$), meaning city $$$x_i$$$ and city $$$y_i$$$ are connected by a road.

The next line contains $$$r$$$ integers separated by spaces  — the cities with rest stops. Each city will appear at most once.

The next line contains $$$v$$$ ($$$1 \le v \le 2 \cdot 10^5$$$)  — the number of vacation plans.

Each of the following $$$v$$$ lines contain two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i, b_i \le n$$$, $$$a_i \ne b_i$$$)  — the start and end city of the vacation plan.

Output:

If Bessie can reach her destination without traveling across more than $$$k$$$ roads without resting for the $$$i$$$-th vacation plan, print YES. Otherwise, print NO.

Sample Input:

6 2 1
1 2
2 3
2 4
4 5
5 6
2
3
1 3
3 5
3 6

Sample Output:

YES
YES
NO

Sample Input:

8 3 3
1 2
2 3
3 4
4 5
4 6
6 7
7 8
2 5 8
2
7 1
8 1

Sample Output:

YES
NO

Note:

The graph for the first example is shown below. The rest stop is denoted by red.

For the first query, Bessie can visit these cities in order: $$$1, 2, 3$$$.

For the second query, Bessie can visit these cities in order: $$$3, 2, 4, 5$$$.

For the third query, Bessie cannot travel to her destination. For example, if she attempts to travel this way: $$$3, 2, 4, 5, 6$$$, she travels on more than $$$2$$$ roads without resting.

The graph for the second example is shown below.