Given two positive integers n and k, return the nth smallest positive integer that has exactly k set bits in its binary representation.

Constraints:

• $1 \leq$ n $\leq 2^{50}$

• $1 \leq$ k $\leq 50$

• The answer is strictly less than $2^{50}$.

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.