Maximize watched duration under consecutive-sum limit

You have a list of videos in a feed. Video i has duration d[i] (positive integer). A user has an “attention span” limit A.

You want to select a subset of videos to watch (keeping the original order, i.e., choose a subsequence of indices i1 < i2 < ... < ik) to maximize total watched time:

$\text{maximize } \sum_{t=1}^{k} d[i_t]$

subject to the constraint that any two consecutively watched videos do not exceed the attention span when added:

$d[i_t] + d[i_{t+1}] \le A \quad \text{for all } t = 1..k-1$

Task

Write an algorithm/function that returns the maximum total watched duration achievable.

Assumptions / clarifications

• n = len(d) can be large enough that brute-forcing all subsets is too slow.
• Watching 0 or 1 video is always allowed.

Follow-up

If the user is allowed to watch the same video multiple times, how would you modify the approach?

• To avoid an unbounded/infinite answer, assume there is an additional limit K = maximum number of videos the user can watch total (including repeats). Return the maximum total watched duration under the same consecutive-sum constraint.