G. Little Artem and Graphtime limit per test12 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle 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.InputFirst 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 ≤ aij < i it is connected to. It is guaranteed that those vertices form a k-clique.OutputOutput a single integer — the number of spanning trees in the given graph modulo 109 + 7.ExamplesInput3 21 2Output3Input4 31 2 3Output16
Input3 21 2
Output3
['*2300']