Give an algorithm with worst-case running time of O(k log k) to print the k biggest elements in a n-element max-heap (binary heap stored in an array) without modifying the max-heap (or if you do modify it, restore it to the input heap within the given time bound). For example, if the max-heap is A = [100, 88, 44, 66, 77, 11, 22, 5, 55] and k = 5, the output could be 100, 88, 66, 77, 55 (the order in which the algorithm prints does not matter). Do not assume n = O(k). Here n can be much larger than k. A correctness proof is not needed (but your pseudocode must be correct). You can use additional data structures. Argue the running time.