Problem Statement 
 There are N trees numbered 0 to N1, and you must plant them along a straight line. Tree i will be planted at coordinate X[i], where X is constructed using the following recursive definition:
X[0] = X0 MOD L
X[i] = (X[i1]*A+B) MOD L (note that X[i1]*A+B may overflow a 32bit integer)
The price of planting tree i is the sum of the distances between tree i and each tree numbered less than i. Calculate the product of the prices of all the trees (except tree 0), and return this number modulo 1,000,000,007. 

Definition 
 Class:  ProductOfPrices  Method:  product  Parameters:  int, int, int, int, int  Returns:  int  Method signature:  int product(int N, int L, int X0, int A, int B)  (be sure your method is public) 




Constraints 
  N will be between 2 and 200,000, inclusive.

  L will be between 1 and 200,000, inclusive.

  X0,A,B will each be between 0 and 1,000,000,000, inclusive.


Examples 
0)  
  Returns: 180  The trees are planted at positions: 3, 4, 5, 6, 7. Their prices are (starting from tree 1): 1, 3, 6, 10. The product of prices is 1 * 3 * 6 * 10 = 180. 


1)  
 
2)  
 
3)  
 
4)  
 5  200000  999999999  123456789  987654321 
 Returns: 499739175  
