InfiniteSequence | Topcoder Archive

Problem Statement

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

A₀ = 1;
A_i = A_[i/p] + A_[i/q] for all i >= 1, where [x] denotes the floor function of x. (see Notes)

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

Definition

Class:: InfiniteSequence
Method:: calc
Parameters:: long, int, int
Returns:: long
Method signature:: long calc(long n, int p, int q)
(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 10^12, inclusive.
p and q will both be between 2 and 10^9, inclusive.

Examples

```
0
```
```
2
```
```
3
```
```
Returns: 1
```
A[0] = 1.
```
7
```
```
2
```
```
3
```
```
Returns: 7
```
A[0] = 1; A[1] = A[0] + A[0] = 2; A[2] = A[1] + A[0] = 2 + 1 = 3; A[3] = A[2] + A[1] = 3 + 2 = 5; A[7] = A[3] + A[2] = 5 + 3 = 8.
```
10000000
```
```
3
```
```
3
```
```
Returns: 32768
```
```
256
```
```
2
```
```
4
```
```
Returns: 89
```
```
1
```
```
1000000
```
```
1000000
```
```
Returns: 2
```

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