Problem Statement 
 A Kshrook is a fairy chess piece that can move horizontally in both directions for at most K squares. Here is an illustration of 2shrook possible moves:
Two Kshrooks attack each other if one of them can reach the other shrook's square in one move. You are given a board with H rows and W columns. Find out the number of ways to place an arbitrary positive amount of Kshrooks on this board so that no two of them attack each other. Return this number modulo 100003.


Definition 
 Class:  ShrooksOnTheBoard  Method:  count  Parameters:  int, int, int  Returns:  int  Method signature:  int count(int K, int H, int W)  (be sure your method is public) 




Constraints 
  K will be between 1 and 1,000,000,000, inclusive. 
  H will be between 1 and 1,000,000,000, inclusive. 
  W will be between 1 and 1,000,000,000, inclusive. 

Examples 
0)  
  Returns: 4  The possible placements are "S..", ".S.", "..S" and "S.S". 


1)  
  Returns: 8  There can not be more than 1 shrook in a row. 


2)  
 