Optimal Prize Collection

You are given a sorted array prizePositions representing the positions of prizes along the X-axis. Each prize has a unique position. Additionally, you are given an integer k. You can select two segments of length k each on the X-axis, such that the segments may intersect. The goal is to maximize the number of prizes you can collect by choosing these two segments optimally.

Print the maximum number of prizes you can win by selecting the two segments wisely.