The English statement was translated by AI and may be slightly different from the original Chinese statement. Please refer to the Chinese statement if you have any questions.

Today, Alice wants to fill a permutation of length $$$n \times m$$$$$$^{\dagger}$$$ into an $$$n \times m$$$ matrix $$$A$$$, such that the sum of numbers in any contiguous submatrix with both height and width at least $$$2$$$ is a composite number.

In other words, for any $$$1 \leq a \lt c \leq n, 1 \leq b \lt d \leq m$$$, Alice wants $$$\sum_{i=a}^{c} \sum_{j=b}^{d} A_{i,j}$$$ to be a composite number.

For example, when $$$n=2$$$ and $$$m=3$$$, matrix $$$B$$$ is a valid construction, while matrix $$$C$$$ is not, because $$$C_{1,2}+C_{1,3}+C_{2,2}+C_{2,3}=17$$$.

$$$$$$ B = \begin{bmatrix} 1 & 3 & 2 \\ 6 & 5 & 4 \end{bmatrix}, \quad C = \begin{bmatrix} 1 & 6 & 2 \\ 3 & 5 & 4 \end{bmatrix} $$$$$$

Given $$$n$$$ and $$$m$$$, can the above requirement be satisfied? If yes, output one valid construction.

$$$^{\dagger}$$$ A permutation of length $$$n$$$ is an array containing the integers from $$$1$$$ to $$$n$$$ exactly once in any order. For example, $$$[2,3,1,5,4]$$$ is a permutation, while $$$[1,2,2]$$$ is not (since $$$2$$$ appears twice), and $$$[1,3,4]$$$ is not (since $$$n=3$$$ but the array contains $$$4$$$).