Imagine you have been given an array of integers, and a query number <code>k</code>. Your task is to write a function that finds all the triplets in the array that sum up to the query number <code>k</code>.

Let’s illustrate this with some examples:

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>nums = [1, 2, 3, 4, 5]
k = 6
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>count_triplets(nums, k) -&gt; 1
</code></pre>

In this case, there is only one triplet that sums up to 6: (1, 2, 3).

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>nums = [10, 10, 20, 30, 40]
k = 60
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>count_triplets(nums, k) -&gt; 3
</code></pre>

In this case, there are three triplets that sum up to 60: (10, 10, 40), (10, 20, 30), and (10, 20, 30).
The value 10 can be retrieved as <code>nums[0]</code> or <code>nums[1]</code>, therefore resulting in two triplets with the same value.

Write a function that returns the number of triplets in the array that sum to `k`.

Triplet Counting

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