Minimize Maximum Adjacent Distance

You are given the positions of N cubes on a 1D line, represented by an array X. You are allowed to remove at most K cubes from this line.

Your goal is to find a configuration of remaining cubes that minimizes the maximum distance between any two adjacent cubes.

For example, if the remaining cubes are at positions [1, 5, 12], the adjacent distances are (5-1)=4 and (12-5)=7. The maximum adjacent distance is 7.

You need to find the minimum possible value for this maximum adjacent distance.

Input Format:

The first line contains two space-separated integers, N (the number of cubes) and K (the maximum number of cubes you can remove).

The second line contains N space-separated integers, representing the positions of the cubes in array X.

Output Format:

Print a single integer representing the minimum possible maximum distance between any two adjacent remaining cubes.

Note:

The problem asks for the "minimum of a maximum," which is a strong indicator for Binary Search.