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/**
 * Brute Force Approach
 * Time Complexity: O(n) for add operation
 * Space Complexity: O(n) for storing all elements
 */
class KthLargestBruteForce {
  /**
   * @param {number} k
   * @param {number[]} nums
   */
  constructor(k, nums) {
    this.k = k;
    this.nums = nums.sort((a, b) => b - a); // Sort in descending order
  }
  
  /**
   * @param {number} val
   * @return {number}
   */
  add(val) {
    // Insert val into the correct position to maintain sorted order
    let i = 0;
    while (i < this.nums.length && this.nums[i] > val) {
      i++;
    }
    this.nums.splice(i, 0, val);
    
    // Return the kth largest element
    return this.nums[this.k - 1];
  }
}
 
/**
 * Min Heap Approach
 * Time Complexity: O(log k) for add operation
 * Space Complexity: O(k) for storing k elements
 * 
 * Note: JavaScript doesn't have a built-in heap, so we'll implement a simple min heap
 */
class MinHeap {
  constructor() {
    this.heap = [];
  }
  
  size() {
    return this.heap.length;
  }
  
  peek() {
    return this.heap[0];
  }
  
  add(val) {
    this.heap.push(val);
    this.bubbleUp(this.heap.length - 1);
  }
  
  poll() {
    if (this.heap.length === 0) {
      return null;
    }
    
    const min = this.heap[0];
    const last = this.heap.pop();
    
    if (this.heap.length > 0) {
      this.heap[0] = last;
      this.bubbleDown(0);
    }
    
    return min;
  }
  
  bubbleUp(index) {
    while (index > 0) {
      const parentIndex = Math.floor((index - 1) / 2);
      if (this.heap[parentIndex] <= this.heap[index]) {
        break;
      }
      
      // Swap parent and current element
      [this.heap[parentIndex], this.heap[index]] = [this.heap[index], this.heap[parentIndex]];
      index = parentIndex;
    }
  }
  
  bubbleDown(index) {
    const lastIndex = this.heap.length - 1;
    
    while (true) {
      const leftChildIndex = 2 * index + 1;
      const rightChildIndex = 2 * index + 2;
      let smallestIndex = index;
      
      if (leftChildIndex <= lastIndex && this.heap[leftChildIndex] < this.heap[smallestIndex]) {
        smallestIndex = leftChildIndex;
      }
      
      if (rightChildIndex <= lastIndex && this.heap[rightChildIndex] < this.heap[smallestIndex]) {
        smallestIndex = rightChildIndex;
      }
      
      if (smallestIndex === index) {
        break;
      }
      
      // Swap current element with the smallest child
      [this.heap[index], this.heap[smallestIndex]] = [this.heap[smallestIndex], this.heap[index]];
      index = smallestIndex;
    }
  }
}
 
class KthLargest {
  /**
   * @param {number} k
   * @param {number[]} nums
   */
  constructor(k, nums) {
    this.k = k;
    this.heap = new MinHeap();
    
    // Add all elements from nums to the heap
    for (const num of nums) {
      this.add(num);
    }
  }
  
  /**
   * @param {number} val
   * @return {number}
   */
  add(val) {
    this.heap.add(val);
    
    // If heap size exceeds k, remove the smallest element
    if (this.heap.size() > this.k) {
      this.heap.poll();
    }
    
    // Return the kth largest element (the root of the heap)
    return this.heap.peek();
  }
}
 
// Test case
const kthLargest = new KthLargest(3, [4, 5, 8, 2]);
console.log(kthLargest.add(3));   // 4
console.log(kthLargest.add(5));   // 5
console.log(kthLargest.add(10));  // 5
console.log(kthLargest.add(9));   // 8
console.log(kthLargest.add(4));   // 8