<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 = [0 for _ in range(len(nums)+1)]
        for i in range(1, len(nums)+1):
            prefixSum[i] = prefixSum[i-1] + nums[i-1]
        maxFromLeft, maxFromRight = [[0, -1] for _ in range(len(nums))], [[0, -1]for _ in range(len(nums))]
        maxFromLeft[0] = [prefixSum[k], 0]
        maxFromRight[-k] = [prefixSum[-1] - prefixSum[-k-1], len(nums)-k]
        j = len(nums) - k - 1
        for i in range(1, len(nums)-k+1):
            maxFromLeft[i] = maxFromLeft[i-1]
            curSum = prefixSum[i+k] - prefixSum[i]
            if curSum > maxFromLeft[i][0]:
                maxFromLeft[i] = [curSum, i]
            maxFromRight[j] = maxFromRight[j+1]
            curSum = prefixSum[j+k] - prefixSum[j]
            if curSum >= maxFromRight[j+1][0]:
                maxFromRight[j] = [curSum, j]
            j -= 1
        maxSum, result = 0, None
        for i in range(k, len(nums)-2*k+1):
            curSum = prefixSum[i+k] - prefixSum[i]
            leftSum, leftIndex = maxFromLeft[i-k]
            rightSum, rightIndex = maxFromRight[i+k]
            if leftSum + rightSum + curSum > maxSum:
                result = [leftIndex, i, rightIndex]
                maxSum = leftSum + rightSum + curSum
        return result
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