1207E · XOR Guessing

Problem: 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.

Output Format: 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.

Note: 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.