Problem Statement

There are $N$ towns numbered $1, 2, \dots, N$, connected by $N-1$ roads.
The $i$-th road connects town $A_i$ and town $B_i$ and has length $1$. From any town, every other town can be reached by traveling along some number of roads.
Simply put, the towns and roads form a tree.

Paken-kun keeps $K$ slimes, and the $i(1\leq i\leq K)$-th slime is initially in town $C_i$.
Slimes may move between towns.

Paken-kun, who holds monster shows while traveling from town to town, wants to know the total distance the slimes travel when, at a given moment, he calls all the slimes to the town he is in.

Paken-kun tried to compute this, but it was very difficult, so he decided to ask you, a renowned competitive programmer.

Paken-kun's request is to process $Q$ queries. There are 2 types of queries, given in the following formats.

Input

$N\ K\ Q$
$C_1\ C_2 \dots C_K$
$A_1\ B_1$
$A_2\ B_2$
$\dots$
$A_{N-1}\ B_{N-1}$
$Query_1$
$Query_2$
$\dots$
$Query_Q$

Output

For each query of the second type, output the total distance on one line, followed by a newline.

Sample

3 2 2
1 3
2 1
3 1
2 3
2 2

1
3

4 2 3
4 3
2 1
3 1
4 2
2 2
1 2 1
2 1

3
2