Graph Counting

Problem code: GRAPHCT

All submissions for this problem are available.

First for some definitions :

Let G = (V,E) be an undirected graph containing an edge e = (u,v) with u ? v. Let f be a function which maps every vertex in V\{u,v} to itself, and otherwise, maps it to a new vertex w. The contraction of e results in a new graph G? = (V?,E?), where V? = (V\{u,v})?{w}, E? = E\{e}, and for every x ? V, x? = f(x) ? V? is incident to an edge e? ? E? if and only if, the corresponding edge, e ? E is incident to x in G.

An undirected graph H is called a minor of the graph G if H is isomorphic to a graph that can be obtained by zero or more edge contractions on a subgraph of G.

A graph is connected if there exists a path between any two vertices. A biconnected graph is one which remains connected even after the removal of any one vertex and all edges incident to it.

A simple graph is one which does not have more than one edge between any pair of vertex, nor does it have an edge from a vertex to itself.

You need to count how many simple biconnected graphs having n vertices and m edges exist such that they do not have a cycle of length 5 as a minor. Two graphs are considered distinct if there exist vertices having labels i and j which are adjacent in the first graph, but not in the second graph.

Input :

The first line contains the number of test cases T. Each of the next lines contains two integers n and m.

Output :

Output T lines, one corresponding to each test case. For a test case, output the number of graphs as described in the question. Output the answer modulo 1000000007.

Sample Input :
5
1 0
3 2
3 3
4 4
5 10


Sample Output :
1
0
1
3
0


Constraints :
1 <= T <= 2000
1 <= n <= 100
0 <= m <= 10000

Author: syco
Date Added: 9-04-2010
Time Limit: 2 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC


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