bobo has a permutation p1,p2,…,pn of 1,2,…,n.
Knowing m extra constraints of form pai<pbi, bobo wanna count the number of different permutations modulo (109+7).
It is guaranteed that there is at least one such permutation.
The input consists of several tests. For each tests:
The first line contains n,m (1≤n≤40,0≤m≤20). Each of the following m lines contain 2 integers ai,bi(1≤ai,bi≤n).
For each tests:
A single number denotes the number of permutations.