CountingSeries | Topcoder Archive

Problem Statement

You are given longs a, b, c and d. The numbers a and b define an arithmetic progression that consists of all numbers of the form a + b*x, where x is a nonnegative integer. Likewise, c and d define a geometric progression that consists of all the numbers that are equal to c * d^y, where y is a nonnegative integer. You are also given a long upperBound. Return the total number of integers between 1 and upperBound, inclusive, that belong to the arithmetic progression, the geometric progression or both.

Definition

Class:: CountingSeries
Method:: countThem
Parameters:: long, long, long, long, long
Returns:: long
Method signature:: long countThem(long a, long b, long c, long d, long upperBound)
(be sure your method is public)

Notes

The ^ operator in this statement denotes the exponentiation operation. For example, 3^0 = 1 and 2^4 = 2*2*2*2 = 16.

Constraints

a, b, c and upperBound will each be between 1 and 1000000000000 (10^12), inclusive.
d will be between 1 and 100000 (10^5), inclusive.

Examples

```
1
```
```
1
```
```
1
```
```
2
```
```
1000
```
```
Returns: 1000
```
The arithmetic progression is: 1, 2, 3, 4, ... . The geometric progression is: 1, 2, 4, 8, 16, ... . Each positive integer is contained in at least one of the progressions.
```
3
```
```
3
```
```
1
```
```
2
```
```
1000
```
```
Returns: 343
```
This time, the arithmetic progression is: 3, 6, 9, 12, ... . The geometric progression is still: 1, 2, 4, 8, 16, .... There are 333 multiples of 3 between 1 and 1000, inclusive, and there are 10 powers of 2, 512 being the highest. As these two progressions do not have any common elements, the total result is 343.
```
40
```
```
77
```
```
40
```
```
100000
```
```
40
```
```
Returns: 1
```
```
452
```
```
24
```
```
4
```
```
5
```
```
600
```
```
Returns: 10
```
The 10 numbers are: 4, 20, 100, 452, 476, 500, 524, 548, 572 and 596.
```
234
```
```
24
```
```
377
```
```
1
```
```
10000
```
```
Returns: 408
```

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