You are given two integers, m and k, and a stream of integers. Your task is to design and implement a data structure that efficiently calculates the MK Average for the stream.

To compute the MK Average, follow these steps:

1. Stream length check: If the stream contains fewer than m elements, return -1 as the MK Average.

2. Window selection: Otherwise, copy the last m elements of the stream to a separate container and remove the smallest k elements and the largest k elements from the container.

3. Average calculation: Calculate the average of the remaining elements (rounded down to the nearest integer).

Implement the MKAverage class

• MKAverage(int m, int k): Initializes the object with integers m and k and an empty stream.

• void addElement(int num): Adds the integer num to the stream.

• int calculateMKAverage(): Returns the current MK Average for the stream as described above, or -1 if the stream contains fewer than m elements.

Constraints:

• $3 <=$ m $<= 10^5$

• $1 <$ k*2 $< m$

• $1 <=$ num $<= 10^5$

• $10^3$ calls will be made to addElement and calculateMKAverage, at most.

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.