Implement k-th largest in a number stream

You are designing a small library to monitor statistics over a stream of integers. Implement a data structure that, given an integer `k` and an initial list of integers, supports the following operation: - `add(val)`: insert the integer `val` into the stream and return the **k-th largest** element among all elements seen so far (including the new one). More formally, after each call to `add`, if you took all numbers that have been provided (both the initial list and all numbers added so far), sorted them in **non-decreasing** order, you should return the element that is `k` positions from the end (the k-th largest). You may assume that `k` is always valid (i.e., there are at least `k` elements after each `add` call). ### API to implement Define a class or type with: - A constructor that takes: - `k` (an integer) - `nums` (a list/array of integers, possibly empty) - A method: - `add(val: int) -> int` that inserts `val` and returns the current k-th largest element. ### Constraints - You may assume: - `1 \le k \le 10^4` - At most `10^4` calls to `add` will be made. - Each integer value fits in a standard 32-bit signed integer. - Your design should be efficient enough to handle the worst-case number of `add` calls within typical interview time complexity expectations. Describe only the code-level behavior and interface; you do **not** need to provide a working implementation here.