<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]:
        n = len(nums)
        cum = 0
        sums = []
        for i in range(1, n+1):
            cum += nums[n-i]
            if i > k:
                cum -= nums[n-i+k]
            if i >= k:
                sums.append(cum)
        #print(sums)
        sums = sums[::-1]
        cur = [(s, (idx,)) for idx, s in enumerate(sums)]
        for _ in range(2):
            #print(cur)
            news = []
            i = len(cur) - k - 1
            cs, cidx = cur[-1]
            while i >= 0:
                s, idx = cur[i+k]
                if s >= cs:
                    cs = s
                    cidx = idx
                news.append((sums[i]+cs, (i, *cidx)))
                i -= 1
            cur = news[::-1]
        #print(cur)
        mv = -1
        rst = []
        for v, idx in cur:
            if v > mv:
                mv = v
                rst = idx
        return list(rst)
        


        
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