| This temple only magnifies the mountain's power. | |
| Badeline | |
| This is an interactive problem. | |
| You are given two positive integers $n$ and $m$ ($\bf{n \le m}$). | |
| The jury has hidden from you a rectangular matrix $a$ with $n$ rows and $m$ columns, where $a_{i,j} \in \\{ -1, 0, 1 \\}$ for all $1 \le i \le n$ and $1 \le j \le m$. The jury has also selected a cell $(i_0, j_0)$. Your goal is to find $(i_0,j_0)$. | |
| In one query, you give a cell $(i, j)$, then the jury will reply with an integer. | |
| * If $(i, j) = (i_0, j_0)$, the jury will reply with $0$. * Else, let $S$ be the sum of $a_{x,y}$ over all $x$ and $y$ such that $\min(i, i_0) \le x \le \max(i, i_0)$ and $\min(j, j_0) \le y \le \max(j, j_0)$. Then, the jury will reply with $|i - i_0| + |j - j_0| + |S|$. | |
| Find $(i_0, j_0)$ by making at most $n + 225$ queries. | |
| Note: the grader is not adaptive: $a$ and $(i_0,j_0)$ are fixed before any queries are made. | |
| Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 50$) — the number of test cases. The description of the test cases follows. | |
| The only line of each test case contains two integers $n$ and $m$ ($1 \le n \le m \le 5000$) — the numbers of rows and the number of columns of the hidden matrix $a$ respectively. | |
| It is guaranteed that the sum of $n \cdot m$ over all test cases does not exceed $25 \cdot 10^6$. | |
| The hidden matrix in the first test case: | |
| $1$| $0$| $1$| $\color{red}{\textbf{0}}$ ---|---|---|--- $1$| $0$| $0$| $1$ $0$| $-1$| $-1$| $-1$ The hidden matrix in the second test case: | |
| $\color{red}{\textbf{0}}$ --- Note that the line breaks in the example input and output are for the sake of clarity, and do not occur in the real interaction. |