CF641G.Little Artem and Graph

Little Artem is given a graph, constructed as follows: start with some $k$ -clique, then add new vertices one by one, connecting them to $k$ already existing vertices that form a $k$ -clique.

Artem wants to count the number of spanning trees in this graph modulo $10^{9}+7$ .

First line of the input contains two integers $n$ and $k$ ( $1<=n<=10000$ , $1<=k<=min(n,5)$ ) — the total size of the graph and the size of the initial clique, respectively.

Next $n-k$ lines describe $k+1$ -th, $k+2$ -th, ..., $i$ -th, ..., $n$ -th vertices by listing $k$ distinct vertex indices 1<=a_{ij}<i it is connected to. It is guaranteed that those vertices form a k-clique.

Output a single integer — the number of spanning trees in the given graph modulo $10^{9}+7$ .