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 109+7.

First line of the input contains two integers n and k (1 \le n \le 10000, 1 \le k \le 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 \le aij \lt 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 109+7.