Guess The Maximums

题意翻译

### 题意简述 本题是**交互题**。 给定长为 $n$ 的数组 $a=[a_1,a_2,...,a_n]$ 和 $k$ 个互不相交的子集 $S_1,S_2,...,S_k$，这些子集中的元素都是 $[1,n]$ 之间的正整数。这些子集两两的**交集**为**空**。 你可以进行最多 $12$ 次询问。每次询问你可以给出 $c$ 个互不相同且在 $[1,n]$ 之间的正整数 $v_1,v_2,...,v_c$，然后你会得到 $\max\{v_i\}$。 对于每个子集 $S_i$，你需要求出 $P_i=\max\limits_{j \notin S_i} a_j$。 ### 输入格式 第一行一个正整数 $t$，表示数据组数。 对于每组数据，第一行两个正整数 $n,k$，表示数组长度和子集数量。 接下来 $k$ 行，每行第一个正整数 $c$ 表示该子集大小，接下来 $c$ 个正整数表示该子集中的元素。 $1 \leq t \le 10,2 \leq n \leq 1000,1 \leq a_i,k \leq n,1 \leq c < n$ ### 交互方式 如果要查询，请打印一行： - `? c ` 后面接上 $c$ 个互不相同且在 $[1,n]$ 之间的正整数 $v_1,v_2,...,v_c$，用空格隔开。在此之后，需要清空缓冲区，此时你可以在标准输入中读到一行一个正整数，表示 $\max\{v_i\}$。 当你提交答案时，需要输出 `! ` 后面接上 $k$ 个正整数 $P_1,P_2,...,P_k$，用空格隔开。在此之后，需要清空缓冲区。此时，如果你的答案正确，则会读到一行一个字符串 `Correct`，否则会读到 `Incorrect`，你不应该忽略它。 翻译 by Meatherm

题目描述

This is an interactive problem. Ayush devised a new scheme to set the password of his lock. The lock has $ k $ slots where each slot can hold integers from $ 1 $ to $ n $ . The password $ P $ is a sequence of $ k $ integers each in the range $ [1, n] $ , $ i $ -th element of which goes into the $ i $ -th slot of the lock. To set the password of his lock, Ayush comes up with an array $ A $ of $ n $ integers each in the range $ [1, n] $ (not necessarily distinct). He then picks $ k $ non-empty mutually disjoint subsets of indices $ S_1, S_2, ..., S_k $ $ (S_i \underset{i \neq j} \cap S_j = \emptyset) $ and sets his password as $ P_i = \max\limits_{j \notin S_i} A[j] $ . In other words, the $ i $ -th integer in the password is equal to the maximum over all elements of $ A $ whose indices do not belong to $ S_i $ . You are given the subsets of indices chosen by Ayush. You need to guess the password. To make a query, you can choose a non-empty subset of indices of the array and ask the maximum of all elements of the array with index in this subset. You can ask no more than 12 queries.

输入输出格式

输入格式

The first line of the input contains a single integer $ t $ $ (1 \leq t \leq 10) $ — the number of test cases. The description of the test cases follows. The first line of each test case contains two integers $ n $ and $ k $ $ (2 \leq n \leq 1000, 1 \leq k \leq n) $ — the size of the array and the number of subsets. $ k $ lines follow. The $ i $ -th line contains an integer $ c $ $ (1 \leq c \lt n) $ — the size of subset $ S_i $ , followed by $ c $ distinct integers in the range $ [1, n] $ — indices from the subset $ S_i $ . It is guaranteed that the intersection of any two subsets is empty.

输出格式

To ask a query print a single line: - In the beginning print "? c " (without quotes) where $ c $ $ (1 \leq c \leq n) $ denotes the size of the subset of indices being queried, followed by $ c $ distinct space-separated integers in the range $ [1, n] $ . For each query, you will receive an integer $ x $ — the maximum of value in the array among all the indices queried. If the subset of indices queried is invalid or you exceeded the number of queries (for example one of the indices is greater than $ n $ ) then you will get $ x = -1 $ . In this case, you should terminate the program immediately. When you have guessed the password, print a single line "! " (without quotes), followed by $ k $ space-separated integers — the password sequence. Guessing the password does not count towards the number of queries asked. After this, you should read a string. If you guess the password correctly, you will receive the string "Correct". In this case, you should continue solving the remaining test cases. If the guessed password is incorrect, you will receive the string "Incorrect". In this case, you should terminate the program immediately. The interactor is not adaptive. The array $ A $ does not change with queries. After printing a query do not forget to output 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 documentation for other languages. ### Hacks To hack the solution use the following test format: The first line of the input should contain a single integer $ t $ $ (1 \leq t \leq 10) $ — the number of test cases. The first line of each test case should contain two integers $ n $ and $ k $ $ (2 \leq n \leq 1000, 1 \leq k \leq n) $ — the size of the array and the number of subsets. The next line should consist of $ n $ space separated integers in the range $ [1, n] $ — the array $ A $ . $ k $ lines should follow. The $ i $ -th line should contain an integer $ c $ $ (1 \leq c \lt n) $ — the size of subset $ S_i $ , followed by $ c $ distinct integers in the range $ [1, n] $ — indices from the subset $ S_i $ . The intersection of any two subsets has to be empty.

输入输出样例

输入样例 #1

1
4 2
2 1 3
2 2 4

1

2

3

4

Correct

输出样例 #1

? 1 1

? 1 2

? 1 3

? 1 4

! 4 3

说明

The array $ A $ in the example is $ [1, 2, 3, 4] $ . The length of the password is $ 2 $ . The first element of the password is the maximum of $ A[2] $ , $ A[4] $ (since the first subset contains indices $ 1 $ and $ 3 $ , we take maximum over remaining indices). The second element of the password is the maximum of $ A[1] $ , $ A[3] $ (since the second subset contains indices $ 2 $ , $ 4 $ ). Do not forget to read the string "Correct" / "Incorrect" after guessing the password.