Sliding Maximum - The Pattern

Use a monotonic decreasing deque. Store indices, not values. The front always holds the index of the current maximum. When processing index $i$: First, remove indices from the front that are outside the window (index $< i - k + 1$).

Second, remove indices from the back while $nums[back] \leq nums[i]$. Third, add $i$ to the back. Why remove smaller elements? Because $nums[i]$ is both larger AND enters later. Those smaller elements will never be the maximum while $nums[i]$ is in the window.