P9727 [EC Final 2022] Aqre

Given an $n \times m$ matrix, you need to fill it with $0$ and $1$, such that: - There cannot be **four** consecutive horizontal or vertical cells filled with the same number. - The cells filled with $1$ form a connected area. (Two cells are adjacent if they share an edge. A group of cells is said to be connected if for every pair of cells it is possible to find a path connecting the two cells which lies completely within the group, and which only travels from one cell to an adjacent cell in each step.) Please construct a matrix satisfying the conditions above and has as many $1$s as possible. Output the maximum number of $1$s, and the matrix.

The first line contains an integer $T~(1\leq T\leq 10^3)$ -- the number of test cases. For each test case, the first line contains two integers $n, m~(2\leq n, m\leq 10^3)$. ### It is guaranteed that the sum of $n\cdot m$ over all test cases does not exceed $10^6$.

For each test case, output the maximum number of $1$s in the first line. Then output the matrix in the following $n$ lines. If there are multiple solution, output any.