You are given an array points containing the coordinates of points on a 2D plane, where points[i] $= [x_i, y_i]$ is sorted by $x$ values in strictly increasing order, and an integer k.

Find and return the maximum value of the equation $y_i + y_j + |x_i - x_j|$ such that $|x_i - x_j| \leq$ k and $1 \leq i < j \leq$ points.length.

It is guaranteed that there exists at least one pair of points that satisfies the condition $|x_i - x_j| \leq$ k.

Constraints:

• $2 \leq$ points.length $\leq 10^5$

• points[i].length $= 2$

• $-10^8 \leq x_i, y_i \leq 10^8$

• $0 \leq$ k $\leq 2 \times 10^8$

• $x_i < x_j$ for all $1 \leq i < j \leq$ points.length

• $x_i$ form a strictly increasing sequence.

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.