InfiniteSequence2 | Topcoder Archive

Problem Statement

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Let's consider an infinite sequence A defined as follows:

A_i = 1 for all i <= 0;
A_i = A_[i/p]-x + A_[i/q]-y for all i >= 1, where [x] denotes the floor function of x. (see Notes)

You will be given n, p, q, x and y. Return the n-th element of A (index is 0-based).

Definition

Class:: InfiniteSequence2
Method:: calc
Parameters:: long, int, int, int, int
Returns:: long
Method signature:: long calc(long n, int p, int q, int x, int y)
(be sure your method is public)

Notes

[x] denotes the floor function of x which returns the highest integer less than or equal to x. For example, [3.4] = 3, [0.6] = 0.

Constraints

n will be between 0 and 10^13, inclusive.
p and q will both be between 2 and 10^9, inclusive.
x and y will both be between 0 and 10^9, inclusive.

Examples

```
10000000
```
```
2
```
```
3
```
```
10000000
```
```
10000000
```
```
Returns: 2
```
A[10000000] = A[-5000000] + A[-6666667] = 2.
```
12
```
```
2
```
```
3
```
```
1
```
```
0
```
```
Returns: 8
```
```
0
```
```
2
```
```
2
```
```
0
```
```
0
```
```
Returns: 1
```
A[0] = 1.
```
123
```
```
45
```
```
67
```
```
8
```
```
9
```
```
Returns: 2
```

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