16F. Secret Trail

• $1 \le n \le 100$
• The hidden graph is simple and undirected.
• The hidden graph is connected.
• Among every $4$ distinct vertices, there is at least one edge.
• You may ask at most $2n$ queries.

The interaction starts with the interactor printing one integer $n$.

You may ask at most $2n$ queries.

To ask a query, print a line in the following format:

$? \ v \ k \ s_1 \ s_2 \ \ldots \ s_k$

Here $1 \le v \le n$, $1 \le k \le n-1$, and $s_1,s_2,\ldots,s_k$ must be distinct vertices different from $v$.

After this, the interactor prints one integer $u$.

If there is at least one vertex in $S=\{s_1,s_2,\ldots,s_k\}$ adjacent to $v$, then $u$ is one such vertex. If there are several possible choices, the interactor may return any of them.

If no vertex in $S$ is adjacent to $v$, then $u=0$.

To give the final answer, print a line in the following format:

$! \ \ell \ p_1 \ p_2 \ \ldots \ p_\ell$

The vertices $p_1,p_2,\ldots,p_\ell$ must be distinct, every two consecutive vertices must be adjacent in the hidden graph, and $\ell$ must be at least $\left\lfloor 2n/3 \right\rfloor+1$.

After printing each query or the final answer, flush the output.