You are given a $0$ indexed integer array nums and an integer k.

In a single operation, you can choose any element in nums and multiply its value by $2$.

Return the maximum possible bitwise OR value of all elements in nums after applying this operation at most k times.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• $1 \leq$ k $\leq 15$

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.