Sum of Maximums of Every Window of Size K

To sum the maximum of every window of size k, maintain a deque of indices whose values are in decreasing order. For each index i, first remove the front if it is outside the window (<= i-k). Then remove back indices while their values are less than or equal to nums[i], because the new value dominates them for all future windows in which both appear. Push i. Once i >= k-1, the front index is the maximum for the current window, so add nums[deque.front] to the answer. Store indices, not only values, so expiration is unambiguous with duplicates. Each index enters and leaves the deque once, giving O(n) time and O(k) space; use a wide accumulator because window maxima may sum beyond a 32-bit integer. Clarify whether ties should preserve older indices; either comparison convention works if expiration is correct.