Kth Largest Element in a Stream

Description

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 kth highest test score after a new score has been submitted. More specifically, we are looking for the kth 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.