Permanent
Description
Little X has solved the #P-complete problem in polynomial time recently. So he gives this task to you.
There is a special n × n matrix A, you should calculate its permanent modulo 1000000007 (109 + 7). The special property of matrix A is almost all its elements equal to 1. Only k elements have specified value.
You can find the definition of permanent at the link: https://en.wikipedia.org/wiki/Permanent
The first line contains two space-separated integers n, k (1 ≤ n ≤ 105; 1 ≤ k ≤ 50).
The next k lines contain the description of the matrix. The i-th line contains three space-separated integers xi, yi, wi (1 ≤ xi, yi ≤ n; 0 ≤ wi ≤ 109). These numbers denote that Axi, yi = wi. All the elements of the matrix except of the given elements are equal to 1.
It's guaranteed that all the positions (xi, yi) are distinct.
Print the permanent of the matrix modulo 1000000007 (109 + 7).
Input
The first line contains two space-separated integers n, k (1 ≤ n ≤ 105; 1 ≤ k ≤ 50).
The next k lines contain the description of the matrix. The i-th line contains three space-separated integers xi, yi, wi (1 ≤ xi, yi ≤ n; 0 ≤ wi ≤ 109). These numbers denote that Axi, yi = wi. All the elements of the matrix except of the given elements are equal to 1.
It's guaranteed that all the positions (xi, yi) are distinct.
Output
Print the permanent of the matrix modulo 1000000007 (109 + 7).
Samples
3 1
1 1 2
8
10 10
3 3 367056794
6 2 124561273
1 3 46718146
6 9 415916869
10 5 985968336
3 1 526792265
1 4 386357058
10 4 349304187
2 7 102032499
3 6 502679075
233333333