D. Strange Device
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$m$$$.

Input

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.

Interaction

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.

Example
Input
4 3
4 9
4 9
4 9
1 2
Output
? 2 3 4
? 1 3 4
? 1 2 4
? 1 2 3
! 3
Note

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