CF1423M.Milutin's Plums

As you all know, the plum harvesting season is on! Little Milutin had his plums planted in an orchard that can be represented as an $n$ by $m$ matrix. While he was harvesting, he wrote the heights of all trees in a matrix of dimensions $n$ by $m$.

At night, when he has spare time, he likes to perform various statistics on his trees. This time, he is curious to find out the height of his lowest tree. So far, he has discovered some interesting properties of his orchard. There is one particular property that he thinks is useful for finding the tree with the smallest heigh.

Formally, let $L(i)$ be the leftmost tree with the smallest height in the $i$-th row of his orchard. He knows that $L(i) \le L(i+1)$ for all $1 \le i \le n - 1$. Moreover, if he takes a submatrix induced by any subset of rows and any subset of columns, $L(i) \le L(i+1)$ will hold for all $1 \le i \le n'-1$, where $n'$ is the number of rows in that submatrix.

Since the season is at its peak and he is short on time, he asks you to help him find the plum tree with minimal height.

众所周知，李子采摘季到了！小米卢廷在他的果园里种了李子树，该果园可以表示为一个 $n$ 行 $m$ 列的矩阵。在采摘过程中，他将每棵树的高度记录在一个 $n$ 行 $m$ 列的矩阵中。

夜晚闲暇时，他喜欢对他的果树进行各种统计分析。这一次，他想找出自己果园中高度最低的那棵树。到目前为止，他已发现果园具有一些有趣的性质。其中有一条性质，他认为对寻找最矮的树特别有用。

形式化地，令 $L(i)$ 表示第 $i$ 行中最矮树中最靠左的那一棵的位置（即列索引）。他已知对所有 $1 \le i \le n - 1$，均有 $L(i) \le L(i+1)$。此外，若任取若干行与若干列构成一个子矩阵，则在该子矩阵中，对任意 $1 \le i \le n'-1$（其中 $n'$ 为该子矩阵的行数），仍有 $L(i) \le L(i+1)$ 成立。

由于采摘季正值高峰，他时间紧迫，因此请你帮助他找出高度最小的李子树。

This problem is interactive.

The first line of input will contain two integers $n$ and $m$, representing the number of rows and the number of columns in Milutin's orchard. It is guaranteed that $1 \le n, m \le 10^6$.

The following lines will contain the answers to your queries.

本题为交互式问题。

输入的第一行包含两个整数 $n$ 和 $m$，分别表示米卢廷果园的行数和列数。保证 $1 \le n, m \le 10^6$。

接下来的若干行将包含对你所提出查询的响应。

Once you know have found the minimum value $r$, you should print ! $r$ to the standard output.

一旦你找到了最小值 $r$，你应该向标准输出打印 ! $r$。