### Problem Statement

NOTE: This problem statement contains superscripts that may not display properly if viewed outside of the applet.

You are given two geometric progressions S1 = (b1*q1i, 0 <= i <= n1-1) and S2 = (b2*q2i, 0 <= i <= n2-1). Return the number of distinct integers that belong to at least one of these progressions.

### Definition

 Class: GeometricProgressions Method: count Parameters: int, int, int, int, int, int Returns: int Method signature: int count(int b1, int q1, int n1, int b2, int q2, int n2) (be sure your method is public)

### Constraints

-b1 and b2 will each be between 0 and 500,000,000, inclusive.
-q1 and q2 will each be between 0 and 500,000,000, inclusive.
-n1 and n2 will each be between 1 and 100,500, inclusive.

### Examples

0)

 `3` `2` `5` `6` `2` `5`
`Returns: 6`
 The progressions in this case are (3, 6, 12, 24, 48) and (6, 12, 24, 48, 96). There are 6 integers that belong to at least one of them: 3, 6, 12, 24, 48 and 96.
1)

 `3` `2` `5` `2` `3` `5`
`Returns: 9`
 This time the progressions are (3, 6, 12, 24, 48) and (2, 6, 18, 54, 162). Each of them contains 5 elements, but integer 6 belongs to both progressions, so the answer is 5 + 5 - 1 = 9.
2)

 `1` `1` `1` `0` `0` `1`
`Returns: 2`
 The progressions are (1) and (0).
3)

 `3` `4` `100500` `48` `1024` `1000`
`Returns: 100500`
 Each element of the second progression belongs to the first progression as well.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=11343

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14429&pm=11343

Chmel_Tolstiy

#### Testers:

PabloGilberto , ivan_metelsky , Smylic

Math, Simulation