You are given an array of positive integers nums and a positive integer k.

A pair (num1, num2) is defined as excellent if both of the following conditions hold:

• Both num1 and num2 are present in nums.

• The sum of the number of set bits in (num1 OR num2) and (num1 AND num2) is greater than or equal to k.

Return the total number of distinct excellent pairs.

Note: Two pairs (a, b) and (c, d) are distinct if $a \neq c$ or $b \neq d$.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• $1 \leq$ k $\leq 60$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.