# 1825. Finding MK Average

<https://leetcode.com/problems/finding-mk-average>

## Description

You are given two integers, `m` and `k`, and a stream of integers. You are tasked to implement a data structure that calculates the **MKAverage** for the stream.

The **MKAverage** can be calculated using these steps:

1. If the number of the elements in the stream is less than `m` you should consider the **MKAverage** to be `-1`. Otherwise, copy the last `m` elements of the stream to a separate container.
2. Remove the smallest `k` elements and the largest `k` elements from the container.
3. Calculate the average value for the rest of the elements **rounded down to the nearest integer**.

Implement the `MKAverage` class:

* `MKAverage(int m, int k)` Initializes the **MKAverage** object with an empty stream and the two integers `m` and `k`.
* `void addElement(int num)` Inserts a new element `num` into the stream.
* `int calculateMKAverage()` Calculates and returns the **MKAverage** for the current stream **rounded down to the nearest integer**.

**Example 1:**

```
**Input**
["MKAverage", "addElement", "addElement", "calculateMKAverage", "addElement", "calculateMKAverage", "addElement", "addElement", "addElement", "calculateMKAverage"]
[[3, 1], [3], [1], [], [10], [], [5], [5], [5], []]
**Output**
[null, null, null, -1, null, 3, null, null, null, 5]
**Explanation**
MKAverage obj = new MKAverage(3, 1); 
obj.addElement(3);        // current elements are [3]
obj.addElement(1);        // current elements are [3,1]
obj.calculateMKAverage(); // return -1, because m = 3 and only 2 elements exist.
obj.addElement(10);       // current elements are [3,1,10]
obj.calculateMKAverage(); // The last 3 elements are [3,1,10].
                          // After removing smallest and largest 1 element the container will be [3].
                          // The average of [3] equals 3/1 = 3, return 3
obj.addElement(5);        // current elements are [3,1,10,5]
obj.addElement(5);        // current elements are [3,1,10,5,5]
obj.addElement(5);        // current elements are [3,1,10,5,5,5]
obj.calculateMKAverage(); // The last 3 elements are [5,5,5].
                          // After removing smallest and largest 1 element the container will be `[5].
 // The average of [5] equals 5/1 = 5, return 5`
```

**Constraints:**

* `3 <= m <= 105`
* `1 <= k*2 < m`
* `1 <= num <= 105`
* At most `105` calls will be made to `addElement` and `calculateMKAverage`.

## ac

```java
```