Interactive Tree ~ Multiplex Coder

This problem is similar to the problem "INTREECTIVE2". The only difference between them is the number of queries allowed — in this problem, up to 21 queries can be made. In Div. 1 and Div. 2 this problem is worth 40 points and "INTREECTIVE2" is worth 60. In Div. 3 this problem is non-scorable.

This is an interactive task

You are given a tree consisting of $N$ nodes, numbered from $1$ to $N$ . Chef selected an arbitrary node and marked it.

Chef gave you a judge to play with, using which you can ask queries about the given tree.

In each query, you give the judge a non-empty set $S$ of nodes. The judge returns $1$ if there exists $u$ and $v$ (not necessarily distinct) such that $u, v \in S$ and the marked node lies on the shortest path from $u$ to $v$ , or $0$ otherwise.

You have to find the marked node.

For each test case, you can use at most 21 queries.

Interaction

Begin the interaction by reading a single integer $T$ denoting the number of test cases. The description of interaction for $T$ test cases follows.
For each test case, first read a single integer $N$ , denoting the number of nodes in the tree.
$N - 1$ lines follow. The $i^{t h}$ of these lines contains two space-separated integers $u_{i}$ and $v_{i}$ , denoting an edge between the nodes $u_{i}$ and $v_{i}$ .
It is guaranteed that the given graph is a tree.
Now you may begin asking queries. To ask a query about a set $S$ of $k$ nodes $v_{1}, v_{2}, \dots, v_{k}$ ( $1 \leq k \leq N, 1 \leq v_{i} \leq N,$ all $v_{i}$ are distinct), output:
? $k$ $v_{1}$ $v_{2}$ $\dots$ $v_{k}$
You will then receive an integer $x$ . $x$ is $1$ if there exists $u$ and $v$ (not necessarily distinct) such that $u, v \in S$ and the marked node lies on the path from $u$ to $v$ , or $0$ otherwise.
When you have found the marked node(say $v$ ), print the answer in the following format:
! $v$
Outputting the answer doesn't count towards the limit of $21$ queries.
If at any time you make an invalid query or exceed the query limit, the interaction is terminated and you will receive a Wrong Answer verdict.
If you receive a Judge Error verdict, that means your program actually has one of many possible errors: an Idleness Limit Exceeded error (it is waiting for input that does not exist), a Runtime error, you asked an invalid query, or possibly some other error.
Don't forget to flush the output after printing each line!

Constraints

$1 \leq T \leq 1000$
$1 \leq N \leq 1000$
The input graph is a tree
Sum of $N$ does not exceed $5 \cdot 10^{4}$ over all test cases
At most $21$ queries can be made.

Sample Interaction

Grader                You
2
2
1 2
                      ? 1 1
0
                      ! 2
4
1 2
1 4
1 3
                      ? 3 1 2 3
1
                      ? 1 3
1
                      ! 3

Explanation

Test case $1$ : After the $1^{s t}$ query, we know that node $1$ hasn't been marked. So, we are left with only one possibility — node $2$ .
Test case $2$ : Chef marked the node 3.