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 ≤ 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. Output a single integer -- the number of spanning trees in the given graph modulo 109 + 7.