GeometricProgressions | Topcoder Archive

Problem Statement

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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

```
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.
```
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.
```
1
```
```
1
```
```
1
```
```
0
```
```
0
```
```
1
```
```
Returns: 2
```
The progressions are (1) and (0).
```
3
```
```
4
```
```
100500
```
```
48
```
```
1024
```
```
1000
```
```
Returns: 100500
```
Each element of the second progression belongs to the first progression as well.

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