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Problem of the day

Given a integer array nums of length ‘N’ and an integer ‘K’, return the number of pairs ‘(i, j)’ such that:

1 <= ‘i’ < ‘j’ <= ‘N’ and ‘nums[i] * nums[j]’ is divisible by ‘K’.

```
‘N’ = 5, ‘K’ = 4, ‘nums’ = [2, 6, 1, 7, 8]
Output: 5
Explanation: (1, 2), (1, 5), (2, 5), (3, 5), and (4, 5) pairs have their products divisible by K.
```

Detailed explanation

```
1 <= 'T' <= 10
1 <= 'N' <= 10^5
1 <= 'K' <= 10^5
1 <= ‘nums[i]’ <= 10^6
It is guaranteed that sum of ‘N’ over all test cases is <= 10^5
Time Limit: 1 sec
```

```
2
4 5
1 2 3 4
5 2
1 2 3 4 5
```

```
0
7
```

```
For the first test case, there is no pair of indices whose corresponding product is divisible by 5.
For the second test case, the seven pairs of indices whose corresponding products are divisible by two are
(1, 2), (1, 4), (2, 3), (2, 4), (2, 5), (3, 4), and (4, 5).
Their products are 2, 4, 6, 8, 10, 12, and 20 respectively.
Other pairs such as (1, 3) and (3, 5) have products 3 and 15, respectively, which are not divisible by 2.
```

```
2
7 3
3 2 6 1 8 4 1
9 6
8 10 2 5 9 6 3 8 2
```

```
11
18
```