Median of a sliding window

Prices stream in. For a fixed window size w, after the window is full report the median of the last w values as it slides forward.

nums = [1, 3, -1, -3, 5, 3], w = 3
windows: [1,3,-1] -> 1 ; [3,-1,-3] -> -1 ; [-1,-3,5] -> -1 ; [-3,5,3] -> 3
-> [1, -1, -1, 3]

Support each slide in $O(\log w)$. Re-sorting each window is $O(w \log w)$ per step.