Can we divide the array into non-overlapping subsequences and simplify the problem?

In the final array, arr[i-k] ≤ arr[i] should hold. We can use this to divide the array into at most k non-overlapping sequences, where arr[i] will belong to the (i%k)th sequence.

Now our problem boils down to performing the minimum operations on each sequence such that it becomes non-decreasing. Our answer will be the sum of operations on each sequence.

Which indices of a sequence should we not change in order to count the minimum operations? Can finding the longest non-decreasing subsequence of the sequence help?