You are given a $0$ indexed integer array nums of length n, and an integer k.

In one operation, you can choose any index i such that $0 \leq i < n and increase nums[i] by $1$.

The array nums is considered beautiful if the maximum element in every subarray of size at least $3$ is greater than or equal to k.

Return the minimum number of increment operations required to make nums beautiful.

Constraints:

• $3 \leq `n` == `nums.length` \leq 10^5$

• $0 \leq `nums[i]` \leq 10^9$

• $0 \leq `k` \leq 10^9$

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.