XOR Guessing
Contest: Educational Codeforces Round 71 (Rated for Div. 2)
Difficulty rating: 1900
Tags: bitmasks, interactive, math

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.

Interaction format:
Before giving the answer, you may submit no more than $$$2$$$ queries. To ask a query, print one line in the following format: $$$?$$$ $$$a_1$$$ $$$a_2$$$ ... $$$a_{100}$$$, where every $$$a_j$$$ should be an integer from the range $$$[0, 2^{14} - 1]$$$. The line should be ended with a line break character. After submitting a query, flush the output and read the answer to your query — the value of $$$a_i \oplus x$$$ for some $$$i \in [1, 100]$$$. No integer can be used in queries more than once.

If you submit an incorrect query (or ask more than $$$2$$$ queries), the answer to it will be one integer $$$-1$$$. After receiving such an answer, your program should terminate immediately — otherwise you may receive verdict "Runtime error", "Time limit exceeded" or some other verdict instead of "Wrong answer".

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

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.

Example input:
0
32

Example output:
? 3 5 6
? 32 24 37
! 5

Editorial:
Suppose all integers we input in some query have the same value in the $$$k$$$-th bit. Then no matter which $$$i$$$ is chosen by the jury, we can always deduce whether the $$$k$$$-th bit in $$$x$$$ is $$$0$$$ or $$$1$$$.
This leads us to a simple solution: divide $$$14$$$ bits of $$$x$$$ into two groups of size $$$7$$$. In the first query, submit $$$100$$$ integers having the same values in the bits from the first group, and deduce the values of these bits in $$$x$$$. In the second query, do the same for the second group. Be careful to avoid submitting the same integer twice.