<p>Given an integer array <code>nums</code> and an integer <code>k</code>, find three non-overlapping subarrays of length <code>k</code> with maximum sum and return them.</p>

<p>Return the result as a list of indices representing the starting position of each interval (<strong>0-indexed</strong>). If there are multiple answers, return the lexicographically smallest one.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,1,2,6,7,5,1], k = 2
<strong>Output:</strong> [0,3,5]
<strong>Explanation:</strong> Subarrays [1, 2], [2, 6], [7, 5] correspond to the starting indices [0, 3, 5].
We could have also taken [2, 1], but an answer of [1, 3, 5] would be lexicographically larger.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,1,2,1,2,1,2,1], k = 2
<strong>Output:</strong> [0,2,4]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;&nbsp;2<sup>16</sup></code></li>
	<li><code>1 &lt;= k &lt;= floor(nums.length / 3)</code></li>
</ul>

class Solution:
    def maxSumOfThreeSubarrays(self, nums: List[int], k: int) -> List[int]:
        prefixSum, sumArray = [0 for _ in range(len(nums)+1)], []
        curSum = 0
        for i in range(len(nums)):
            prefixSum[i+1] = prefixSum[i] + nums[i]
            curSum += nums[i]
            if i >= k:
                curSum -= nums[i-k]
            if i >= k - 1:
                sumArray.append(curSum)
        maxFromRight, maxFromLeft = [[] for _ in range(len(sumArray))], [[] for _ in range(len(sumArray))]
        maxFromRight[-1] = [sumArray[-1], len(nums)-k]
        maxFromLeft[0] = [sumArray[0], 0]
        for i in range(1, len(sumArray)):
            j = len(sumArray) - i - 1
            maxFromLeft[i] = maxFromLeft[i-1]
            if sumArray[i] > maxFromLeft[i][0]:
                maxFromLeft[i] = [sumArray[i], i]
            maxFromRight[j] = maxFromRight[j+1]
            if sumArray[j] >= maxFromRight[j][0]:
                maxFromRight[j] = [sumArray[j], j]
        resultSum, result = 0, None
        for i in range(k, len(nums)-2*k+1):
            leftMax, leftMaxIndex = maxFromLeft[i-k][0], maxFromLeft[i-k][1]
            rightMax, rightMaxIndex = maxFromRight[i+k][0], maxFromRight[i+k][1]
            curSum = leftMax+rightMax+prefixSum[i+k]-prefixSum[i]
            index = (leftMaxIndex, i, rightMaxIndex)
            if curSum > resultSum:
                resultSum = curSum
                result = index
            if curSum == resultSum and index < result:
                result = index
        return [i for i in result]

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