G. Little Artem and Graph
time limit per test
12 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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

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

Examples
Input
3 21 2
Output
3
Input
4 31 2 3
Output
16