<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]:
        sump = 0
        for i, n in enumerate(nums):
            sump += n
            nums[i] = sump
        
        return self.dfs(0, nums, 3, k, {})[1]

    def dfs(self, idx, nums, kLeft, k, memo):
        # print(f'idx {idx} kLeft {kLeft}')
        if kLeft == 0:
            return 0, []
        if idx > len(nums) - k:
            return 0, []

        if (idx, kLeft) in memo:
            return memo[(idx, kLeft)]

        newSumTakeOthers, newIndicesTakeOthers = self.dfs(idx + k, nums, kLeft - 1, k, memo)
        newSumTake = newSumTakeOthers + (nums[idx + k - 1] if idx == 0 else nums[idx + k - 1] - nums[idx - 1])

        newSumNotTake, newIndicesNotTake = self.dfs(idx + 1, nums, kLeft, k, memo)

        if newSumTake >= newSumNotTake:
            # print(f'take {idx} {[idx] + newIndicesTakeOthers}')
            memo[(idx, kLeft)] = (newSumTake, [idx] + newIndicesTakeOthers )
        else:
            # print(f'not take {idx} {[idx] + newIndicesTakeOthers}')
            memo[(idx, kLeft)] = (newSumNotTake, newIndicesNotTake)
        return memo[(idx, kLeft)]
        

31300