Maximum Sum With Exactly K Elements
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> and an integer <code>k</code>. Your task is to perform the following operation <strong>exactly</strong> <code>k</code> times in order to maximize your score:</p>

<ol>
	<li>Select an element <code>m</code> from <code>nums</code>.</li>
	<li>Remove the selected element <code>m</code> from the array.</li>
	<li>Add a new element with a value of <code>m + 1</code> to the array.</li>
	<li>Increase your score by <code>m</code>.</li>
</ol>

<p>Return <em>the maximum score you can achieve after performing the operation exactly</em> <code>k</code> <em>times.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5], k = 3
<strong>Output:</strong> 18
<strong>Explanation:</strong> We need to choose exactly 3 elements from nums to maximize the sum.
For the first iteration, we choose 5. Then sum is 5 and nums = [1,2,3,4,6]
For the second iteration, we choose 6. Then sum is 5 + 6 and nums = [1,2,3,4,7]
For the third iteration, we choose 7. Then sum is 5 + 6 + 7 = 18 and nums = [1,2,3,4,8]
So, we will return 18.
It can be proven, that 18 is the maximum answer that we can achieve.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,5,5], k = 2
<strong>Output:</strong> 11
<strong>Explanation:</strong> We need to choose exactly 2 elements from nums to maximize the sum.
For the first iteration, we choose 5. Then sum is 5 and nums = [5,5,6]
For the second iteration, we choose 6. Then sum is 5 + 6 = 11 and nums = [5,5,7]
So, we will return 11.
It can be proven, that 11 is the maximum answer that we can achieve.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 100</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 100</code></li>
	<li><code>1 &lt;= k &lt;= 100</code></li>
</ul>

<p>&nbsp;</p>
<style type="text/css">.spoilerbutton {display:block; border:dashed; padding: 0px 0px; margin:10px 0px; font-size:150%; font-weight: bold; color:#000000; background-color:cyan; outline:0; 
}
.spoiler {overflow:hidden;}
.spoiler > div {-webkit-transition: all 0s ease;-moz-transition: margin 0s ease;-o-transition: all 0s ease;transition: margin 0s ease;}
.spoilerbutton[value="Show Message"] + .spoiler > div {margin-top:-500%;}
.spoilerbutton[value="Hide Message"] + .spoiler {padding:5px;}
</style>
Greedy; Array
function maximizeSum(nums: number[], k: number): number {
    const x = Math.max(...nums);
    return k * x + (k * (k - 1)) / 2;
}
