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<sup class="upper-index">9</sup> + 7.
First line of the input contains two integers *n* and *k* (1 ≤ *n* ≤ 10 000, 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*<sub class="lower-index">*ij*</sub> &lt; *i* it is connected to. It is guaranteed that those vertices form a k-clique.
none
print("_RANDOM_GUESS_1689251192.870065")# 1689251192.870094