Sereja and Salesman

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Read problems statements in Mandarin Chinese, Russian and Vietnamese as well.
Sereja has an undirected graph on N vertices. There are edges between all but M pairs of vertices.
A permutation p on the vertices of the graph is represented as p[1], p[2], … , p[N] such that for all i, p[i] is a vertex of the graph. A permutation is called connected if there is an edge between vertices p[i] and p[i+1] for all natural numbers i less than N. Sereja wants to know the number of connected permutations on the graph vertices.
Input
First line of input contains a single integer T, denoting the number of test cases. T tests follow. First line of each test case contains two integers, N and M. M lines follow, each containing a pair of indices of vertices, indicating that those vertices are not connected by an edge.
Output
For each test case, output one number — the answer for the problem modulo 10^{9}+7.
Constraints
 1 ≤ T ≤ 10
 1 ≤ N ≤ 10^{5}
 0 ≤ M ≤ 7
Subtasks
 Subtask #1: 1 ≤ N ≤ 10 (25 points)
 Subtask #2: 1 ≤ N ≤ 100 (25 points)
 Subtask #3: 1 ≤ N ≤ 1000 (25 points)
 Subtask #4: original (25 points)
Example
Input: 2 4 3 1 2 2 3 3 4 2 1 1 2 Output: 2 0
Author:  sereja 
Tester:  antoniuk1 
Editorial  http://discuss.codechef.com/problems/SEAKAM 
Tags  combinatorics, jan16, medium, sereja 
Date Added:  14102014 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, CLOJ, FS 
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