You are given an integer array nums of length n, and two integers k and m.

In one operation, you can choose any element in nums and increment its value by $1$. You can perform at most k operations in total across all elements.

Your goal is to select a subset of m elements from nums such that after performing at most k operations, the bitwise AND of the selected m elements is maximized.

Return the maximum possible bitwise AND of the chosen m elements.

Constraints:

• $1 \leq n ==$ nums.length $\leq 5 imes 10^4$

• $1 \leq$ nums[i] $\leq 10^9$

• $1 \leq$ k $\leq 10^9$

• $1 \leq$ m $\leq n$

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.