Problem Statement 
 Young Andrew has just learned about quadratic equations. He was quite amazed by the fact that their
solutions could look like (5+sqrt(3))/4, so he wants to dig into this issue. More specifically, given five numbers x, y, d, z and k, he wants to find the number of equations a*t^{2}+b*t+c=0 such that (x+y*sqrt(d))/z is a solution of the equation (i.e., when substituting it for t the equation holds) and a, b and c are integers, k <= a, b, c <= k. Notice that the equations he's looking for are not necessarily quadratic, i.e., a is allowed to be zero, as is b and/or c. 

Definition 
 Class:  QuadraticEquations  Method:  howMany  Parameters:  int, int, int, int, int  Returns:  long  Method signature:  long howMany(int x, int y, int d, int z, int k)  (be sure your method is public) 




Constraints 
  x, y and z will be between 1000 and 1000, inclusive. 
  z will not be equal to 0. 
  d will be between 1 and 1000, inclusive. 
  k will be between 0 and 1000000 (10^{6}), inclusive. 

Examples 
0)  
  Returns: 3  The three possible equations are:
0*x^{2}+0*x+0=0, 8*x^{2}20*x+11=0, 8*x^{2}+20*x11=0 


1)  
  Returns: 1  The equation 0*x^{2}+0*x+0=0 always holds. 


2)  
  Returns: 7  The value described is simply 2. The equations are 0*x^{2}+0*x+0=0, 0*x^{2}+1*x2=0, 0*x^{2}1*x+2=0, 1*x^{2}1*x2=0, 1*x^{2}+1*x+2=0, 1*x^{2}2*x+0=0, 1*x^{2}+2*x+0=0. 


3)  
 
4)  
 
5)  
 