<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]:
        s = 0
        cumsum = [(s:=s+j) for j in nums]
        cumsum.insert(0,0)
        sums = [cumsum[i] - cumsum[i-k] for i in range(k,len(cumsum)) ]
       
        max_left = 0
        left_maxes =[]
        for i in range(0,len(sums)):
            if(sums[i]>sums[max_left]):
                max_left = i
                left_maxes.append(max_left)
            else:
                left_maxes.append(max_left)
        max_left = len(sums)-1
        print(sums)
        print(left_maxes)
        right_maxes = [0] * len(sums)
        for i in range(len(sums)-1,0,-1):
            if(sums[i]>=sums[max_left]):
                max_left = i
                right_maxes[i] = max_left
            else:
                right_maxes[i] = max_left
        dp = sums
        print(right_maxes)
        res = [-1,-1,-1]
        maxsum = -1
        i = k
        while((i+k)<=(len(nums)-k)):
            l= dp[left_maxes[i-k]] 
            print(i+k)
            r = dp[right_maxes[i+k]] 
            m = dp[i]
            sum = l+r+m
            
            if(sum > maxsum):
                res[0] = left_maxes[i-k]
                res[2] = right_maxes[i+k]
                res[1] = i
                maxsum = sum
            i = i+1
        return(res)
            
            





        

        
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