Kth Largest Element in a Stream

You are part of a university admissions office and need to keep track of the `kth` highest test score from applicants in real-time. This helps to determine cut-off marks for interviews and admissions dynamically as new applicants submit their scores. You are tasked to implement a class which, for a given integer `k`, maintains a stream of test scores and continuously returns the `k`th highest test score **after** a new score has been submitted. More specifically, we are looking for the `k`th highest score in the sorted list of all scores. Implement the `KthLargest` class: - `KthLargest(int k, int[] nums)` Initializes the object with the integer `k` and the stream of test scores `nums`. - `int add(int val)` Adds a new test score `val` to the stream and returns the element representing the `kth` largest element in the pool of test scores so far.   **Example 1:** **Input:** ["KthLargest", "add", "add", "add", "add", "add"] [[3, [4, 5, 8, 2]], [3], [5], [10], [9], [4]] **Output:** [null, 4, 5, 5, 8, 8] **Explanation:** KthLargest kthLargest = new KthLargest(3, [4, 5, 8, 2]); kthLargest.add(3); // return 4 kthLargest.add(5); // return 5 kthLargest.add(10); // return 5 kthLargest.add(9); // return 8 kthLargest.add(4); // return 8 **Example 2:** **Input:** ["KthLargest", "add", "add", "add", "add"] [[4, [7, 7, 7, 7, 8, 3]], [2], [10], [9], [9]] **Output:** [null, 7, 7, 7, 8] **Explanation:** KthLargest kthLargest = new KthLargest(4, [7, 7, 7, 7, 8, 3]); kthLargest.add(2); // return 7 kthLargest.add(10); // return 7 kthLargest.add(9); // return 7 kthLargest.add(9); // return 8   **Constraints:** - `0 <= nums.length <= 104` - `1 <= k <= nums.length + 1` - `-104 <= nums[i] <= 104` - `-104 <= val <= 104` - At most `104` calls will be made to `add`.