<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 {
public:
    vector<int32_t> maxSumOfThreeSubarrays(vector<int32_t>& nums, int32_t k) {
        int32_t n = nums.size();
        vector<int64_t> prefixSum(n + 1, 0);
        for (int32_t i = 0; i < n; i++) {
            prefixSum[i + 1] = prefixSum[i] + nums[i];
        }
        vector<int64_t> prefixMax(n, 0), suffixMax(n, 0);
        vector<int32_t> prefixIndex(n, 0), suffixIndex(n, 0);

        int64_t tempSum = prefixSum[k] - prefixSum[0];
        prefixMax[k - 1] = tempSum;
        prefixIndex[k - 1] = 0;

        for (int32_t i = k; i < n; i++) {
            int64_t currentSum = prefixSum[i + 1] - prefixSum[i - k + 1];

            if (currentSum > prefixMax[i - 1]) {
                prefixMax[i] = currentSum;
                prefixIndex[i] = i - k + 1;
            } else {
                prefixMax[i] = prefixMax[i - 1];
                prefixIndex[i] = prefixIndex[i - 1];
            }
        }
        
        int64_t tempSuffixSum = prefixSum[n] - prefixSum[n - k];
        suffixMax[n - k] = tempSuffixSum;
        suffixIndex[n - k] = n - k;

        for (int32_t i = n - k - 1; i >= 0; i--) {
            int64_t currentSum = prefixSum[i + k] - prefixSum[i];
            if (currentSum >= suffixMax[i + 1]) {
                suffixMax[i] = currentSum;
                suffixIndex[i] = i;
            } else {
                suffixMax[i] = suffixMax[i + 1];
                suffixIndex[i] = suffixIndex[i + 1];
            }
        }
        
        vector<int32_t> result(3, -1);
        int64_t maxSum = 0;
        for (int32_t i = k; i <= n - 2 * k; i++) {
            int32_t leftIndex = prefixIndex[i - 1];
            int32_t rightIndex = suffixIndex[i + k];
            int64_t currentSum = (prefixSum[i + k] - prefixSum[i]) + prefixMax[i - 1] + suffixMax[i + k];
            if (currentSum > maxSum) {
                maxSum = currentSum;
                result = {leftIndex, i, rightIndex};
            } else if (currentSum == maxSum) {
                vector<int32_t> candidate = {leftIndex, i, rightIndex};
                if (candidate < result) {
                    result = candidate;
                }
            }
        }
        return result;
    }
};
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