AnArray | Topcoder Archive

Problem Statement

One day, Bob the Coder was wondering whether abstract programming problems can have applications in practice. The next day, he was selected to be on a quiz show. He will win one million dollars if he answers the following question:

Given a int[] A with N elements and an int K, count the number of tuples (p, q, r) such that 0 <= p < q < r < N and A[p] * A[q] * A[r] is divisible by K.

Please compute and return the answer to Bob's question.

Definition

Class:: AnArray
Method:: solveProblem
Parameters:: int[], int
Returns:: int
Method signature:: int solveProblem(int[] A, int K)
(be sure your method is public)

Constraints

A will contain between 3 and 2,000 elements, inclusive.
K will be between 1 and 1,000,000, inclusive.
Each element of A will be between 1 and 100,000,000, inclusive.

Examples

```
{31, 1, 3, 7, 2, 5}
```
```
30
```
```
Returns: 1
```
The return value is 1 because there is exactly one valid tuple. The tuple is (2, 4, 5). It is valid because A[2] * A[4] * A[5] = 3 * 2 * 5 = 30.
```
{4, 5, 2, 25}
```
```
100
```
```
Returns: 2
```
```
{100000000, 100000000, 100000000}
```
```
1000000
```
```
Returns: 1
```
Note that the product A[p] * A[q] * A[r] doesn't have to fit into a 64-bit integer variable.

{269, 154, 94, 221, 171, 154, 50, 210, 258, 358, 121, 159, 8, 47, 290, 125, 291, 293, 338, 248, 295, 160, 268, 227, 99, 4, 273}

Returns: 114

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

Returns: 220

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