CF1466I.The Riddle of the Sphinx

What walks on four feet in the morning, two in the afternoon, and three at night?

This is an interactive problem. This problem doesn't support hacks.

Sphinx's duty is to guard the city of Thebes by making sure that no unworthy traveler crosses its gates. Only the ones who answer her riddle timely and correctly (or get an acc for short) are allowed to pass. As of those who fail, no one heard of them ever again...

So you don't have a choice but to solve the riddle. Sphinx has an array $a_1, a_2, \ldots, a_n$ of nonnegative integers strictly smaller than $2^b$ and asked you to find the maximum value among its elements. Of course, she will not show you the array, but she will give you $n$ and $b$. As it is impossible to answer this riddle blindly, you can ask her some questions. For given $i, y$, she'll answer you whether $a_i$ is bigger than $y$. As sphinxes are not very patient, you can ask at most $3 \cdot (n + b) $ such questions.

Although cunning, sphinxes are honest. Even though the array can change between your queries, answers to the previously asked questions will remain valid.

什么东西早上用四只脚走路，中午用两只脚走路，晚上用三只脚走路？

这是一个交互式问题。本题不支持 Hack。

斯芬克斯的职责是守卫底比斯城，确保没有不配的旅人穿过它的城门。只有那些及时且正确地回答出她谜题（简称“AC”）的人，才被允许通过。至于那些失败者，再无人听说过他们的下落……

因此，你别无选择，只能解开这个谜题。斯芬克斯拥有一个长度为 $n$ 的非负整数数组 $a_1, a_2, \ldots, a_n$，其中每个元素严格小于 $2^b$，她要求你找出该数组中元素的最大值。当然，她不会直接向你展示这个数组，但会告诉你 $n$ 和 $b$ 的值。由于盲目作答是不可能的，你可以向她提出若干问题：对于给定的 $i$ 和 $y$，她会回答 $a_i$ 是否大于 $y$。然而，斯芬克斯缺乏耐心，你最多只能提出 $3 \cdot (n + b)$ 个这样的问题。

尽管狡黠，斯芬克斯却诚实守信。即使在你提问过程中该数组可能发生变化，此前所有已提出问题的答案仍将保持有效。

The first line contains two integers $n$ and $b$ ($1 \leq n, b \leq 200$). The remaining parts of the input will be given throughout the interaction process.

第一行包含两个整数 $n$ 和 $b$（$1 \leq n, b \leq 200$）。输入的其余部分将在交互过程中给出。

In all examples, the sequence is fixed beforehand.

In the first example, the sequence is $2, 1, 4, 0, 6$.

In the second example, the sequence is $0, 0, 0, 0$.

In the third example, the sequence is $0$.

Note that if the interactor was adaptive, then the interaction in the first and the third example would not be sufficient to return the correct value of maximum.

在所有示例中，序列均预先固定。

在第一个示例中，序列为 $2, 1, 4, 0, 6$。

在第二个示例中，序列为 $0, 0, 0, 0$。

在第三个示例中，序列为 $0$。

注意：若交互器是自适应的，则第一个和第三个示例中的交互不足以返回正确的最大值。