D. Hemose in ICPC ?time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis is an interactive problem!In the last regional contest Hemose, ZeyadKhattab and YahiaSherif — members of the team Carpe Diem — did not qualify to ICPC because of some unknown reasons. Hemose was very sad and had a bad day after the contest, but ZeyadKhattab is very wise and knows Hemose very well, and does not want to see him sad.Zeyad knows that Hemose loves tree problems, so he gave him a tree problem with a very special device.Hemose has a weighted tree with n nodes and n-1 edges. Unfortunately, Hemose doesn't remember the weights of edges.Let's define Dist(u, v) for u\neq v as the greatest common divisor of the weights of all edges on the path from node u to node v.Hemose has a special device. Hemose can give the device a set of nodes, and the device will return the largest Dist between any two nodes from the set. More formally, if Hemose gives the device a set S of nodes, the device will return the largest value of Dist(u, v) over all pairs (u, v) with u, v \in S and u \neq v.Hemose can use this Device at most 12 times, and wants to find any two distinct nodes a, b, such that Dist(a, b) is maximum possible. Can you help him?InteractionBegin the interaction from reading a single integer n (2 \le n \le 10^3) — the number of nodes in the tree.Next, read n-1 lines. The i-th of the next n-1 lines contains two integers u_i and v_i (1 \leq u_i, v_i \leq n, u_i\neq v_i), which means that there's an edge between nodes u_i and v_i.It's guaranteed that weights of edges were \leq 10^9.It is guaranteed that the given graph is a tree.Now you may begin asking queries. To ask a query about a set of k nodes v_1, v_2, \ldots, v_k (2 \le k \le n, 1 \le v_i \le n, all v_i are distinct), output: ? k v_1 v_2 \ldots v_kYou will then receive an integer x, the largest Dist(v_i, v_j) over 1 \le i, j \le k with i \neq j.When you have found a and b (1 \le a, b \le n), a\neq b) such that Dist(a, b) is the maximum possible, print the answer in the following format: ! a b Outputting answer doesn't count towards the limit of 12 queries.If there are several pairs (a, b) with the same largest Dist(a, b), you can output any.After printing a query do not forget to output the end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use: fflush(stdout) or cout.flush() in C++; System.out.flush() in Java; flush(output) in Pascal; stdout.flush() in Python; see the documentation for other languages.HacksTo hack a solution, use the following format.The first line should contain a single integer n (2 \leq n \le 10^3) — the number of nodes.The i-th of the next n-1 lines should contain three integers u_i, v_i, w_i (1 \le u_i, v_i \le n, u_i\ne v_i, 1 \le w \le 10^9), which means that there's an edge between nodes u_i and v_i with weight w_i.These n-1 edges must form a tree.ExampleInput
6
1 2
2 3
2 4
1 5
5 6

10

2

10Output
? 6 1 2 3 4 5 6

? 3 3 1 5

? 2 1 2

! 1 2NoteThe tree in the first sample:
6
1 2
2 3
2 4
1 5
5 6

10

2

10
? 6 1 2 3 4 5 6  ? 3 3 1 5  ? 2 1 2  ! 1 2
['binary search', 'dfs and similar', 'implementation', 'interactive', 'math', 'number theory', 'trees', '*2300']