You are given an array points containing the coordinates of points on a 2D plane, sorted by the x-values, where points[i] = [x_i, y_i] such that x_i < x_j for all 1 <= i < j <= points.length. You are also given an integer k.

Return the maximum value of the equation y_i + y_j + |x_i - x_j| where |x_i - x_j| <= k and 1 <= i < j <= points.length.

It is guaranteed that there exists at least one pair of points that satisfy the constraint |x_i - x_j| <= k.

Example 1:

Input: points = [[1,3],[2,0],[5,10],[6,-10]], k = 1
Output: 4
Explanation: The first two points satisfy the condition |x_i - x_j| <= 1 and if we calculate the equation we get 3 + 0 + |1 - 2| = 4. Third and fourth points also satisfy the condition and give a value of 10 + -10 + |5 - 6| = 1.
No other pairs satisfy the condition, so we return the max of 4 and 1.

Example 2:

Input: points = [[0,0],[3,0],[9,2]], k = 3
Output: 3
Explanation: Only the first two points have an absolute difference of 3 or less in the x-values, and give the value of 0 + 0 + |0 - 3| = 3.

Constraints:

2 <= points.length <= 10⁵
points[i].length == 2
-10⁸ <= x_i, y_i <= 10⁸
0 <= k <= 2 * 10⁸
x_i < x_j for all 1 <= i < j <= points.length
x_i form a strictly increasing sequence.

Max Value of Equation

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