HIGH  Highways
In some countries building highways takes a lot of time... Maybe that's because there are many possiblities to construct a network of highways and engineers can't make up their minds which one to choose. Suppose we have a list of cities that can be connected directly. Your task is to count how many ways there are to build such a network that between every two cities there exists exactly one path. Two networks differ if there are two cities that are connected directly in the first case and aren't in the second case. At most one highway connects two cities. No highway connects a city to itself. Highways are twoway.
Input
The input begins with the integer t, the number of test cases (equal to about 1000). Then t test cases follow. The first line of each test case contains two integers, the number of cities (1<=n<=12) and the number of direct connections between them. Each next line contains two integers a and b, which are numbers of cities that can be connected. Cities are numbered from 1 to n. Consecutive test cases are separated with one blank line.
Output
The number of ways to build the network, for every test case in a separate line. Assume that when there is only one city, the answer should be 1. The answer will fit in a signed 64bit integer.
Example
Sample input: 4 4 5 3 4 4 2 2 3 1 2 1 3 2 1 2 1 1 0 3 3 1 2 2 3 3 1 Sample output: 8 1 1 3
hide comments
KotoriItsuka:
20150317 02:08:59
ĺťşčŽŽä˝żç¨MatrixTreeĺŽç 

Prime:
20150311 15:20:54
Please use the long long in output 

ankit singh:
20140918 00:38:49
plz explain case1 how it is coming 8....i am getting 6?? 

Ice Lee:
20130629 14:30:46
Damn! WA all the time... 
Added by:  Piotr Łowiec 
Date:  20040702 
Time limit:  7s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 