<p>You are given an integer <code>finalSum</code>. Split it into a sum of a <strong>maximum</strong> number of <strong>unique</strong> positive even integers.</p>

<ul>
	<li>For example, given <code>finalSum = 12</code>, the following splits are <strong>valid</strong> (unique positive even integers summing up to <code>finalSum</code>): <code>(12)</code>, <code>(2 + 10)</code>, <code>(2 + 4 + 6)</code>, and <code>(4 + 8)</code>. Among them, <code>(2 + 4 + 6)</code> contains the maximum number of integers. Note that <code>finalSum</code> cannot be split into <code>(2 + 2 + 4 + 4)</code> as all the numbers should be unique.</li>
</ul>

<p>Return <em>a list of integers that represent a valid split containing a <strong>maximum</strong> number of integers</em>. If no valid split exists for <code>finalSum</code>, return <em>an <strong>empty</strong> list</em>. You may return the integers in <strong>any</strong> order.</p>

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

<pre>
<strong>Input:</strong> finalSum = 12
<strong>Output:</strong> [2,4,6]
<strong>Explanation:</strong> The following are valid splits: <code>(12)</code>, <code>(2 + 10)</code>, <code>(2 + 4 + 6)</code>, and <code>(4 + 8)</code>.
(2 + 4 + 6) has the maximum number of integers, which is 3. Thus, we return [2,4,6].
Note that [2,6,4], [6,2,4], etc. are also accepted.
</pre>

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

<pre>
<strong>Input:</strong> finalSum = 7
<strong>Output:</strong> []
<strong>Explanation:</strong> There are no valid splits for the given finalSum.
Thus, we return an empty array.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> finalSum = 28
<strong>Output:</strong> [6,8,2,12]
<strong>Explanation:</strong> The following are valid splits: <code>(2 + 26)</code>, <code>(6 + 8 + 2 + 12)</code>, and <code>(4 + 24)</code>. 
<code>(6 + 8 + 2 + 12)</code> has the maximum number of integers, which is 4. Thus, we return [6,8,2,12].
Note that [10,2,4,12], [6,2,4,16], etc. are also accepted.
</pre>

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

<ul>
	<li><code>1 &lt;= finalSum &lt;= 10<sup>10</sup></code></li>
</ul>

class Solution:
    def maximumEvenSplit(self, finalSum: int) -> List[int]:
        """
            pass

            if num is odd we return []

            if its even
            2 take not take

            take not take

            28
            k = 1

            2 4

            2, 4, 6, 8

            12 

            2, 4            8

            
        """

        if finalSum % 2 != 0:
            return []

        res = []
        num = 2
        total = 0

        while total + 2 * num + 2 <= finalSum:
            res.append(num)
            total += num
            num += 2
            
        res.append(finalSum - total)

        return res

        # res = [finalSum]
        # k = 2

        # while True:
        #     current_res = []
        #     for i in range(k - 1):
        #         current_res.append(2 * (i + 1))
        #     diff = finalSum - sum(current_res)
        #     if diff <= current_res[-1]:
        #         return res
        #     else:
        #         current_res.append(diff)
        #         res = current_res
        #         k += 1
        


        
306