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.

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

YES
YES
NO

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

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.