Problem - Constrained Subsequence Sum

Given an integer array $nums$ and an integer $k$, return the maximum sum of a non-empty subsequence such that for every two consecutive integers in the subsequence, $nums[i]$ and $nums[j]$, where $i < j$, the condition $j - i \leq k$ is satisfied.

You're solving a dynamic programming problem where the transition looks at the last $k$ states. A naive DP is $O(nk)$. With a monotonic deque, it's $O(n)$.