Problem Statement 
 f is a function from integers to integers. In other words, f is defined over integers, and f(x) is an integer for all integers x. You are given an integer C. f is called Cbeautiful if the following equality is satisfied for all integers x:
Return the minimal possible value of the following formula when f is Cbeautiful:
Use the following recursive definitions to generate the sequences x and y:
 x[0] = xzero
 For all integer i between 1 and N1, inclusive, x[i] = (x[i1] * xprod + xadd) % xmod
 y[0] = yzero
 For all integer i between 1 and N1, inclusive, y[i] = (y[i1] * yprod + yadd) % ymod


Definition 
 Class:  FunctionalEquation  Method:  minAbsSum  Parameters:  int, int, int, int, int, int, int, int, int, int  Returns:  long  Method signature:  long minAbsSum(int C, int N, int xzero, int xprod, int xadd, int xmod, int yzero, int yprod, int yadd, int ymod)  (be sure your method is public) 




Notes 
  64bit integers should be used to generate the sequences x and y to avoid overflow. 

Constraints 
  C will be between 1 and 16, inclusive. 
  N will be between 1 and 10,000, inclusive. 
  xmod and ymod will each be between 1 and 1,000,000,000, inclusive. 
  xzero, xprod and xadd will each be between 0 and xmod  1, inclusive. 
  yzero, yprod and yadd will each be between 0 and ymod  1, inclusive. 

Examples 
0)  
  Returns: 0  f(x) = x + 1 is a 3beautiful function.
Since x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and y = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
the sum of f(x[i])  y[i] is 0. 


1)  
  Returns: 5  x and y are the same as in example 0, but f(x) = x + 1 is not a 4beautiful function. 


2)  
 16  10000  654816386  163457813  165911619  987654321  817645381  871564816  614735118  876543210 
 Returns: 3150803357206  
