Matrix Modulo

An $N\times N$ matrix $B$ is called **$K$-strange** if it satisfies the following conditions:- - Each integer from $1$ to $N^2$ appears *exactly once* in $B$; and - If every element of $B$ is reduced modulo $K$, the resulting matrix is symmetric. Formally, that means $B_{i, j} \bmod K = B_{j, i} \bmod K$ for every $1 \leq i, j \leq N$; where $x\bmod y$ denotes the remainder obtained upon dividi