Compute moving and weighted averages from a stream

You are processing a stream of numeric events (e.g., user activity counts). You are given a fixed window size `X`. ## Part 1: Moving average over last X values Design a data structure / function that supports: - `next(value) -> avg` where `avg` is the average of the **most recent `X` values** seen so far (or fewer than `X` if fewer values have arrived). ## Part 2 (follow-up): Weighted moving average Modify the approach to compute a **weighted moving average** over the most recent `X` values where **more recent values have higher weight**. For example, for the last `k <= X` values (oldest to newest): - weights could be `1, 2, ..., k` - weighted average = \(\frac{\sum_{i=1}^{k} i \cdot v_i}{\sum_{i=1}^{k} i}\) ### Constraint Do this **without storing all previous data points** (i.e., memory should not grow with the total stream length).