CF1207E.XOR Guessing

This is an interactive problem. Remember to flush your output while communicating with the testing program. You may use fflush(stdout) in C++, system.out.flush() in Java, stdout.flush() in Python or flush(output) in Pascal to flush the output. If you use some other programming language, consult its documentation. You may also refer to the guide on interactive problems: https://codeforces.com/blog/entry/45307.

The jury picked an integer $x$ not less than $0$ and not greater than $2^{14} - 1$. You have to guess this integer.

To do so, you may ask no more than $2$ queries. Each query should consist of $100$ integer numbers $a_1$, $a_2$, ..., $a_{100}$ (each integer should be not less than $0$ and not greater than $2^{14} - 1$). In response to your query, the jury will pick one integer $i$ ($1 \le i \le 100$) and tell you the value of $a_i \oplus x$ (the bitwise XOR of $a_i$ and $x$). There is an additional constraint on the queries: all $200$ integers you use in the queries should be distinct.

It is guaranteed that the value of $x$ is fixed beforehand in each test, but the choice of $i$ in every query may depend on the integers you send.

这是一个交互式问题。在与评测程序通信时，请务必刷新你的输出。你可以在 C++ 中使用 fflush(stdout)，在 Java 中使用 system.out.flush()，在 Python 中使用 stdout.flush()，或在 Pascal 中使用 flush(output) 来刷新输出。如果你使用其他编程语言，请查阅其相关文档。你也可以参考交互式问题指南：https://codeforces.com/blog/entry/45307。

出题人预先选定一个整数 $x$，满足 $0 \le x \le 2^{14} - 1$。你需要猜出这个整数。

为此，你最多可以提出 $2$ 次询问。每次询问需包含 $100$ 个整数 $a_1, a_2, \dots, a_{100}$（每个整数均需满足 $0 \le a_j \le 2^{14} - 1$）。对于你的每次询问，出题人将从中选择一个下标 $i$（$1 \le i \le 100$），并告诉你 $a_i \oplus x$ 的值（即 $a_i$ 与 $x$ 的按位异或结果）。此外，对询问还有一个额外约束：你在两次询问中总共使用的 $200$ 个整数必须互不相同。

保证在每个测试用例中，$x$ 的值是预先固定好的；但每次询问中出题人选择的下标 $i$ 可能依赖于你发送的整数。

To give the answer, your program should print one line $!$ $x$ with a line break in the end. After that, it should flush the output and terminate gracefully.

要给出答案，您的程序应打印一行 $!$ $x$，并在末尾换行。之后，程序应刷新输出并正常终止。

The example of interaction is not correct — you should sumbit exactly $100$ integers in each query. Everything else is correct.

Hacks are forbidden in this problem.

交互示例不正确——您应在每次查询中恰好提交 100 个整数。其余内容均正确。

本题禁止 Hack。