### 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*t2+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 (106), inclusive.

### Examples

0)

 `5` `1` `3` `4` `30`
`Returns: 3`
 The three possible equations are: 0*x2+0*x+0=0, 8*x2-20*x+11=0, -8*x2+20*x-11=0
1)

 `5` `1` `3` `4` `10`
`Returns: 1`
 The equation 0*x2+0*x+0=0 always holds.
2)

 `2` `0` `1` `1` `2`
`Returns: 7`
 The value described is simply 2. The equations are 0*x2+0*x+0=0, 0*x2+1*x-2=0, 0*x2-1*x+2=0, 1*x2-1*x-2=0, -1*x2+1*x+2=0, 1*x2-2*x+0=0, -1*x2+2*x+0=0.
3)

 `0` `-1` `4` `-1` `2`
`Returns: 7`
 It is still 2.
4)

 `-1` `3` `3` `2` `1000000`
`Returns: 153847`
5)

 `2` `0` `1` `3` `5`
`Returns: 11`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6832

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10007&pm=6832

Petr

#### Testers:

PabloGilberto , brett1479 , Olexiy , ged

Math