Problem Statement 
 Fox Ciel likes to jump around in large fields. She is currently at point (0, 0) of a field, and she wants to land at point (Tx, Ty) using exactly R jumps.
In one jump, she can move 0, 1, 2, ..., Mx units in the positive x direction and 0, 1, 2, ..., My units in the positive y direction. All jumps must have a nonzero distance. In addition, there are some jumps which she is not good at. These jumps are described in the int[] bad. If bad contains the number b, it means she cannot make a diagonal jump where she moves exactly b units in the positive x direction and b units in the positive y direction. Each element of bad will be a multiple of 10.
For instance, if Mx=12, My=11, bad={10} and she is at point (0, 0), then the only points she can jump to are the green ones shown below:
Return the number of ways she can start at (0, 0), jump exactly R times, and land at (Tx, Ty), modulo 10,007. Two ways are considered to be different if there is an index i, 0 <= i < R, such that Ciel lands at different points after the ith (0based) jump in these ways. 

Definition 
 Class:  FoxJumping  Method:  getCount  Parameters:  int, int, int, int, int, int[]  Returns:  int  Method signature:  int getCount(int Tx, int Ty, int Mx, int My, int R, int[] bad)  (be sure your method is public) 




Constraints 
  Tx and Ty will each be between 1 and 800, inclusive. 
  Mx and My will each be between 1 and 800, inclusive. 
  R will be between 1 and 1,600, inclusive. 
  bad will contain between 0 and 50 elements, inclusive. 
  Each element of bad will be between 1 and min(Mx, My), inclusive, and be a multiple of 10. 
  All elements of bad will be distinct. 

Examples 
0)  
  Returns: 1  There is only 1 way to reach the destination.



1)  
  Returns: 6  The following are the 6 ways she can reach her destination. Note that when she jumps, she must move a distance of at least one unit.



2)  
  Returns: 1  She can jump only once, so there is 1 way to reach the destination. 


3)  
  Returns: 0  This case is almost the same as the previous one. However, in this case, the required jump is a bad jump, so she cannot reach the destination in a single jump. 


4)  
 
5)  
 123  456  70  80  90  {30, 40, 20, 10, 50} 
 Returns: 6723  
