Strange Device

题意翻译

有一个长为 $n$ 数列 $a$，值已确定且值互不相等，但是你不知道。 现在有个设备，你可以输入长为 $k$ 的上升序列 $p_1,p_2 \dots p_k$，进行询问，它会回答 $a_{p_1},a_{p_2} \dots a_{p_k}$ 中第 $m$ 小的数在原数列的坐标和这个数的值。现在给你 $n$ 和 $k$，让你在最多询问 $n$ 次后回答 $m$ 的大小。保证一定可以构造出方案。

题目描述

This problem is interactive. We have hidden an array $ a $ of $ n $ pairwise different numbers (this means that no two numbers are equal). You can get some information about this array using a new device you just ordered on Amazon. This device can answer queries of the following form: in response to the positions of $ k $ different elements of the array, it will return the position and value of the $ m $ -th among them in the ascending order. Unfortunately, the instruction for the device was lost during delivery. However, you remember $ k $ , but don't remember $ m $ . Your task is to find $ m $ using queries to this device. You can ask not more than $ n $ queries. Note that the array $ a $ and number $ m $ are fixed before the start of the interaction and don't depend on your queries. In other words, interactor is not adaptive. Note that you don't have to minimize the number of queries, and you don't need to guess array $ a $ . You just have to guess $ m $ .

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ ( $ 1\le k < n \le 500 $ ) — the length of the array and the number of the elements in the query. It is guaranteed that number $ m $ satisfies $ 1\le m \le k $ , elements $ a_1, a_2, \dots, a_n $ of the array satisfy $ 0\le a_i \le 10^9 $ , and all of them are different.

输出格式

You begin the interaction by reading $ n $ and $ k $ . To ask a question about elements on positions $ x_1, x_2, \dots, x_k $ , in a separate line output $ ? $ $ x_1 $ $ x_2 $ $ x_3 $ ... $ x_k $ Numbers in the query have to satisfy $ 1 \le x_i \le n $ , and all $ x_i $ have to be different. Don't forget to 'flush', to get the answer. In response, you will receive two integers $ pos $ and $ a_{pos} $ — the position in the array $ a $ of the $ m $ -th in ascending order element among $ a_{x_1}, a_{x_2}, \dots, a_{x_k} $ , and the element on this position. In case your query is invalid or you asked more than $ n $ queries, the program will print $ -1 $ and will finish interaction. You will receive a Wrong answer verdict. Make sure to exit immediately to avoid getting other verdicts. When you determine $ m $ , output $ ! $ $ m $ 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. Hack format For the hacks use the following format: The first line has to contain three integers $ n, k, m $ ( $ 1 \le m \le k < n \le 500 $ ) — the length of the array, number of elements in the query, and which in the ascending order number the device returns. In the next line output $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 0\le a_i \le 10^9 $ ) — the elements of the array. They have to be pairwise different.

输入输出样例

输入样例 #1

4 3
4 9
4 9
4 9
1 2

输出样例 #1

? 2 3 4
? 1 3 4
? 1 2 4
? 1 2 3
! 3

说明

In the example, $ n = 4 $ , $ k = 3 $ , $ m = 3 $ , $ a = [2, 0, 1, 9] $ .