Problem Statement

Ebi-chan and Kiri-chan play the cat game. The cat game is a game in which cats are moved on a tree. The tree has $N$ vertices and $N-1$ edges. The vertices are numbered from $1$ to $N$, and the $i\ (1\le i \le N-1)$-th edge connects vertex $u_i$ and vertex $v_i$. There are $M$ cats, and initially the $i\ (1\le i\le M)$-th cat is at vertex $A_i$.
Starting with Ebi-chan, they alternately perform the following operation.

• Choose one cat and move it to an adjacent vertex. However, it cannot be moved to a vertex where that cat has been before (because the cat would get bored).

Input

$N\ M$
$A_1\ A_2\ \cdots\ A_M$
$u_1\ v_1$
$u_2\ v_2$
$\vdots$
$u_{N-1}\ v_{N-1}$

All inputs are integers.
$1 \le N \le 2 \times 10^5$
$1 \le M \le 2 \times 10^5$
$1 \le u_i,\ v_i\le N\ (1\le i\le N-1)$
$u_i\neq v_i\ (1\le i\le N-1)$
$1 \le A_i\le N\ (1\le i\le M)$
The given graph is guaranteed to be a tree.

Output

$i\ v$

$i$ and $v$ are integers and must satisfy either "$1\le i\le M$ and $1\le v\le N$" or $i=v=-1$.
The meaning of the output is as follows.

If Ebi-chan has a winning strategy
Output one of the best first moves. If the move takes the $i$-th cat to vertex $v$, output $i$ and $v$ separated by a space.
If there are multiple best moves, you may output any of them.

If Kiri-chan has a winning strategy
Let $i=v=-1$ and output "-1 -1".

Print a newline at the end.

Sample

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

1 4

1 2
1 1

-1 -1