A window into a matrix is a contiguous sub matrix.

Consider a $16\times n$ matrix where every entry is either $0$ or $1$. Let $B(k,n)$ be the total number of these matrices such that the sum of the entries in every $2\times k$ window is $k$.

You are given that $B(2,4)=65550$ and $B(3,9)\equiv 87273560(\mathrm{mod}1000000007)$.

Find $B({10}^5,{10}^{16})$. Give your answer modulo $1000000007$.