T514577 Strange Homura Game (English ver.)

[Chinese statement](https://www.luogu.com.cn/problem/T469289). **You must submit your code at the Chinese version of the statement.**

**This problem is differ from B1. You had better read both statements.** **This is an interactive problem.** **Hint:** We provide a formalized description of this problem at the end of the statement. Homura and Madoka are playing a game. Homura has thought of a positive integer $m$, and Madoka need to determine its value.. It is guaranteed that $\textcolor{red}{2}\le m\le 10^{17}$. Also, Homura doesn't cheat, that is, **Madoka wouldn't change the value of $m$** during the whole game. Madoka can ask Homura: for a **non-negative** integer $x$, what is the value of $x\bmod m$. Madoka aimed to determine the value of $m$ with the number of queries as small as possible. (In order to get full points, you need to solve this problem within $2$ queries.) The game will be played for $T$ rounds. However, Madoka is at the military training, so she turned to you. **Formally,** there exists a hidden positive integer $m\in [\textcolor{red}{2},10^{17}]$. In each query, a **non-negative** integer $x$ is given, and it returns $x \bmod m$. Find $m$ with the least number of queries. There are $T$ test cases. The value of $m$ is read from input file and won't change according to queries. That is, **the interactor is non-adaptive.** ### Implementation Details Input a positive integer $T$ first, which stands for the number of the rounds. For each test case: - Output a single line containing $\texttt{? }x$ to make a query. Then, an integer indicating $x\bmod m$ is available. $x$ is a **positive** integer should be guaranteed, and $x$ must fall in $ \textcolor{red} {[0,10^{18}]}$. If $x=-1$ instead of the answer, it means that the query limit is excceeded, or the query is invalid. The solution should quit immediately. - Output a single line containing $\texttt{! }m$ to respond to the guess. After outputting the queries, do not forget to output a newline character and flush the output buffer. Otherwise, you will receive the verdict TLE. To flush the buffer, use: - `fflush(stdout)` or `cout.flush()` in C++; - `flush(output)` in Pascal; - `stdout.flush()` in Python; - refer to the documentation for other languages.

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#### Constraints It is guaranteed that - $1\le T\le 100$; - $m$ is a positive ineteger, and $\textcolor{red}{2}\le m\le 10^{17}$。 #### Scoring Let $Q$ be the maximum queries used in each test. The $\mathrm{score}$ is calculated as following: $$ \begin{aligned} \mathrm{score}=\begin{cases} 0, & Q\in [101,+\infty) \\ 30, & Q\in [3,101) \\ 50, & Q\in [0,3) \\ \end{cases} \end{aligned} $$ The score of the task is the minimum score of each test.