Score : $550$ points

问题描述

这是一个 交互式任务（在此任务中，您的程序与裁判通过标准输入和输出进行交互）。

您已知一个整数 $N$ 和一个 奇数 $K$。
裁判手中有一个隐藏的长度为 $N$ 的序列 $A = (A_1, A_2, \dots, A_N)$，其中包含 $0$ 和 $1$。

虽然您不能直接访问序列 $A$ 的元素，但您最多可以向裁判提出 $N$ 次以下查询：

• 选择 $1$ 到 $N$ 之间互不相同的整数 $x_1, x_2, \dots$, 和 $x_K$，询问 $A_{x_1} + A_{x_2} + \dots + A_{x_K}$ 的奇偶性。

通过最多 $N$ 次查询确定 $(A_1, A_2, \dots, A_N)$ 并打印答案。
这里需要注意的是，裁判是自适应的。换句话说，只要修改后的序列与过去查询的回答保持一致，裁判可以随时修改 $A$ 序列的内容。
因此，只有当满足以下条件时，您的程序才被视为正确，否则视为错误：

• 您的程序打印出与当前为止所有查询回答一致的序列，并且这是唯一符合这一条件的序列。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

This is an interactive task (where your program and the judge interact via Standard Input and Output).

You are given an integer $N$ and an odd number $K$.
The judge has a hidden length-$N$ sequence $A = (A_1, A_2, \dots, A_N)$ consisting of $0$ and $1$.

While you cannot directly access the elements of sequence $A$, you are allowed to ask the judge the following query at most $N$ times.

• Choose distinct integers $x_1, x_2, \dots$, and $x_K$ between $1$ and $N$, inclusive, to ask the parity of $A_{x_1} + A_{x_2} + \dots + A_{x_K}$.

Determine $(A_1, A_2, \dots, A_N)$ by at most $N$ queries, and print the answer.
Here, the judge is adaptive. In other words, the judge may modify the contents of $A$ as long as it is consistent with the responses to the past queries.
Therefore, your program is considered correct if the output satisfies the following condition, and incorrect otherwise:

• your program prints a sequence consistent with the responses to the queries so far, and that is the only such sequence.

Constraints

• $1 \leq K \lt N \leq 1000$
• $K$ is odd.
• $A_i$ is $0$ or $1$.

Input and Output

This is an interactive task (where your program and the judge interact via Standard Input and Output).

First of all, receive $N$ and $K$ from Standard Input.

$N$ $K$

Then, repeat asking queries until you can uniquely determine $(A_1, A_2, \dots, A_N)$.

Each query should be printed to Standard Output in the following format, where $x_1, x_2, \dots$, and $x_K$ are $K$ distinct integers between $1$ and $N$, inclusive.

$?$ $x_1$ $x_2$ $\dots$ $x_K$

The response to the query is given from Standard Input in the following format.

$T$

Here, $T$ denotes the response to the query.

• $T$ is 0 when $A_{x_1} + A_{x_2} + \dots + A_{x_K}$ is even, and

• $T$ is 1 when $A_{x_1} + A_{x_2} + \dots + A_{x_K}$ is odd.

However, if $x_1, x_2, \dots$ and $x_K$ do not satisfy the constraints, or the number of queries exceeds $N$, then $T$ is -1.

If the judge returns -1, your program is already considered incorrect, so terminate the program immediately.

When you can determine all the elements of $A$, print those elements in the following format, and terminate the program immediately.

$!$ $A_1$ $A_2$ $\dots$ $A_N$

Notes

• Print a newline and flush Standard Output at the end of each message. Otherwise, you may get a TLE verdict.
• The verdict will be indeterminate if there is malformed output during the interaction or your program quits prematurely.
• Terminate the program immediately after printing the answer, or the verdict will be indeterminate.
• The judge for this problem is adaptive. This means that the judge may modify the contents of $A$ as long as it is consistent with the responses to the past queries.

Sample Interaction

In the following interaction, $N=5$ and $K=3$. Note that the following output itself will result in WA.
Here, $A = (1, 0, 1, 1, 0)$ is indeed consistent with the responses, but so is $(0, 0, 1, 0, 0)$, so sequence $A$ is not uniquely determined. Thus, this program is considered incorrect.

Input	Output	Description
5 3		First, you are given integers $N$ and $K$.
	? 2 4 1	You ask a query with $(x_1, x_2, x_3) = (2, 4, 1)$.
0		The response to the query is $0$, so the judge returns that value.
	? 5 3 2	You ask a query with $(x_1, x_2, x_3) = (5, 3, 2)$.
1		The response to the query is $1$, so the judge returns that value.
	! 1 0 1 1 0	You print $(1, 0, 1, 1, 0)$ to guess $A$. Since sequence $A$ is not uniquely determined, the verdict will be WA.

update @ 2024/3/10 08:55:34