Solve Running Median of K Elements using Lua Language

Given an array of integers and a positive integer K, return an array of K integers where each element represents the median of all previous elements including itself. For an odd number of integers, the median is the middle element after sorting. For an even number of integers, the median is the average of the two middle elements after sorting (round down to nearest integer).

Constraints:

• K ≤ arr.length ≤ 10⁵
• 1 ≤ K ≤ 10⁴
• -10⁶ ≤ arr[i] ≤ 10⁶
• The solution should run in O(K log K) time

Examples:

Input: arr = [1,4,3,2,6,5,8,7], K = 4
Output: [1,2,3,2]
Explanation:
First element: median of [1] is 1
Second element: median of [1,4] is 2
Third element: median of [1,4,3] is 3
Fourth element: median of [1,4,3,2] is 2

Input: arr = [5,2,8,1,9], K = 3
Output: [5,3,5]
Explanation:
First element: median of [5] is 5
Second element: median of [5,2] is 3
Third element: median of [5,2,8] is 5