CF1520F1.Guess the K-th Zero (Easy version)

This is an interactive problem.

This is an easy version of the problem. The difference from the hard version is that in the easy version $t=1$ and the number of queries is limited to $20$.

Polycarp is playing a computer game. In this game, an array consisting of zeros and ones is hidden. Polycarp wins if he guesses the position of the $k$-th zero from the left $t$ times.

Polycarp can make no more than $20$ requests of the following type:

• ? $l$ $r$ — find out the sum of all elements in positions from $l$ to $r$ ($1 \le l \le r \le n$) inclusive.

In this (easy version) of the problem, this paragraph doesn't really make sense since $t=1$ always. To make the game more interesting, each guessed zero turns into one and the game continues on the changed array. More formally, if the position of the $k$-th zero was $x$, then after Polycarp guesses this position, the $x$-th element of the array will be replaced from $0$ to $1$. Of course, this feature affects something only for $t \gt 1$.

Help Polycarp win the game.

Interaction

First, your program must read two integers $n$ and $t$ ($1 \le n \le 2 \cdot 10^5$, $t=1$).

Then $t$ lines follow, each of which contains one integer $k$ ($1 \le k \le n$). It is guaranteed that at the moment of the request the array contains at least $k$ zeros. In order to get the next value of $k$, you must output the answer for the current value of $k$.

After that, you can make no more than $20$ requests.

Use the following format to output the answer (it is not a request, it doesn't count in $20$):

• ! $x$ — position of the $k$-th zero.

Positions in the array are numbered from left to right from $1$ to $n$ inclusive.

After printing $t$ answers, your program should exit immediately.

In this task, the interactor is not adaptive. This means that within the same test, the hidden array and the queries do not change.

In case of an incorrect query, -1 will be displayed. When this value is received, your program must immediately exit normally (for example, by calling exit(0)), otherwise, the testing system may issue an arbitrary verdict.

If the number of requests is exceeded, the verdict wrong answer will be displayed.

Your solution may get the verdict Idleness limit exceeded if you don't print anything or forget to flush the output buffer.

To flush the output buffer, you need to do the following immediately after the query output and the end-of-line character:

• fflush(stdout) or cout.flush() in C ++;
• System.out.flush() in Java;
• flush(output) in Pascal;
• stdout.flush() in Python;
• see the documentation for other languages.

Hacks

Use the following format for hacks:

On the first line print the string $s$ ($1 \le |s| \le 2 \cdot 10^5$), consisting of zeros and ones, and an integer $t$ ($t = 1$) — hidden array and number of requests, respectively. In the next $t$ lines output the number $k$ ($1 \le k \le |s|$).

The hacked solution will not have direct access to the hidden array.

这是一个交互式问题。

这是该问题的简单版本。与困难版本的区别在于：在简单版本中，$t=1$，且查询次数限制为 $20$ 次。

Polycarp 正在玩一款电脑游戏。游戏中隐藏着一个仅由 $0$ 和 $1$ 组成的数组。Polycarp 若能 $t$ 次猜中从左往右数第 $k$ 个 $0$ 的位置，即获胜。

Polycarp 最多可进行 $20$ 次如下形式的查询：

• ? l r — 查询位置从 $l$ 到 $r$（包含端点，$1 \le l \le r \le n$）的所有元素之和。

在本题（简单版本）中，由于恒有 $t = 1$，下述段落实际上并无实际意义。为使游戏更有趣，每次成功猜中的 $0$ 都会变为 $1$，游戏在更新后的数组上继续进行。更准确地说，若第 $k$ 个 $0$ 的位置为 $x$，则 Polycarp 猜中该位置后，数组的第 $x$ 个元素将由 $0$ 变为 $1$。显然，此特性仅在 $t > 1$ 时才产生影响。

请帮助 Polycarp 获胜。

交互流程

首先，你的程序需读入两个整数 $n$ 和 $t$（$1 \le n \le 2 \cdot 10^5$，$t = 1$）。

随后输入 $t$ 行，每行一个整数 $k$（$1 \le k \le n$）。保证在请求该 $k$ 值时，数组中至少存在 $k$ 个 $0$。为获取下一个 $k$ 值，你必须先输出当前 $k$ 对应的答案。

之后，你最多可进行 $20$ 次查询。

使用如下格式输出答案（这不是一次查询，不计入 $20$ 次限制内）：

• ! x — 第 $k$ 个 $0$ 的位置。

数组中位置编号从左至右，依次为 $1$ 到 $n$（含端点）。

输出全部 $t$ 个答案后，你的程序应立即终止。

本题的交互器是非自适应的。这意味着在同一测试用例中，隐藏数组及所有查询均保持不变。

若发出非法查询，将返回 $-1$。一旦收到该值，你的程序必须立即正常退出（例如调用 exit(0)），否则评测系统可能给出任意错误结果。

若查询次数超出限制，将判为“答案错误”。

若你的程序未输出任何内容或忘记刷新输出缓冲区，则可能得到“空闲时间超限”（Idleness limit exceeded）的判定。

为刷新输出缓冲区，请在输出查询语句及换行符后立即执行以下操作：

• C++ 中：fflush(stdout) 或 cout.flush()；
• Java 中：System.out.flush()；
• Pascal 中：flush(output)；
• Python 中：stdout.flush()；
• 其他语言请参阅相应文档。

Hack 方法

Hack 输入格式如下：

第一行输入字符串 $s$（$1 \le |s| \le 2 \cdot 10^5$），仅由 $0$ 和 $1$ 组成，以及一个整数 $t$（$t = 1$）——分别表示隐藏数组和请求次数。接下来 $t$ 行，每行一个整数 $k$（$1 \le k \le |s|$）。

被 Hack 的程序无法直接访问隐藏数组。

In the first test, the $[1, 0, 1, 1, 0, 1]$ array is hidden. In this test $k=2$.

在第一个测试中，隐藏的数组为 $[1, 0, 1, 1, 0, 1]$。本测试中 $k=2$。