GRIDCOIN  Placing Coins on a Grid
In how many ways can R coins be placed on an N * M grid such that each row and each column have atleast 1 coin ?
Input :
The first line contains the number of test cases T. T lines follow containing 3 integers: N,M and R. (1 <= T <= 100. 1 <= N,M <= 200. 1 <= R <= N * M)
Output :
Output T lines, one for each test case, containing the output for the corresponding test case. Output all values modulo 1000000007
Sample Input :
3
1 1 1
2 1 1
2 3 3
Sample Output :
1
0
6
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Varun Jalan:
20100928 07:06:15
yes 

Madhusudhanan D`:
20100928 07:06:15
Are the coins identical? 

Varun Jalan:
20100928 07:06:15
no 

Madhusudhanan D`:
20100928 07:06:15
Can a grid contain more than 1 coin? 
Added by:  Varun Jalan 
Date:  20100912 
Time limit:  0.256s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS OBJC VB.NET 
Resource:  own problem 