For integers $m,n$ ($0\le n<m$), let $L(m,n)$ be an $m\times m$ grid with the top-right $n\times n$ grid removed.

For example, $L(5,3)$ looks like this:

We want to number each cell of $L(m,n)$ with consecutive integers $1,2,3,\dots$ such that the number in every cell is smaller than the number below it and to the left of it.

For example, here are two valid numberings of $L(5,3)$:

Let $\mathrm{LC}(m,n)$ be the number of valid numberings of $L(m,n)$.
It can be verified that $\mathrm{LC}(3,0)=42$, $\mathrm{LC}(5,3)=250250$, $\mathrm{LC}(6,3)=406029023400$ and $\mathrm{LC}(10,5)mod76543217=61251715$.

Find $\mathrm{LC}(10000,5000)mod76543217$.