1def maxSumOfThreeSubarrays(nums, k):
2    n = len(nums)
3    prefix = [0] * (n + 1)
4    for i in range(1, n + 1):
5        prefix[i] = prefix[i - 1] + nums[i - 1]
6    left = [0] * n
7    right = [0] * n
8    for i in range(k, n):
9        if prefix[i + 1] - prefix[i + 1 - k] > prefix[left[i - 1] + k] - prefix[left[i - 1]]:
10            left[i] = i + 1 - k
11        else:
12            left[i] = left[i - 1]
13    for i in range(n - k - 1, -1, -1):
14        if prefix[i + k] - prefix[i] >= prefix[right[i + 1] + k] - prefix[right[i + 1]]:
15            right[i] = i
16        else:
17            right[i] = right[i + 1]
18    max_sum = 0
19    ans = [-1, -1, -1]
20    for mid in range(k, n - 2 * k + 1):
21        l, r = left[mid - 1], right[mid + k]
22        total_sum = (prefix[l + k] - prefix[l]) + (prefix[mid + k] - prefix[mid]) + (prefix[r + k] - prefix[r])
23        if total_sum > max_sum:
24            max_sum = total_sum
25            ans = [l, mid, r]
26    return ans
27
28# Example usage
29nums = [1, 2, 1, 2, 6, 7, 5, 1]
30k = 2
31print(maxSumOfThreeSubarrays(nums, k))

1#include <vector>
using namespace std;

vector<int> maxSumOfThreeSubarraysDP(vector<int>& nums, int k) {
    int n = nums.size();
    vector<int> dp(n, 0);
    vector<int> prefix(n + 1, 0);
    vector<int> left(n), right(n);

    for (int i = 0; i < n; ++i) {
        prefix[i + 1] = prefix[i] + nums[i];
    }

    for (int i = 0; i < k; ++i) {
        dp[i] = prefix[i + 1];
    }

    for (int i = k; i < n; ++i) {
        if (prefix[i + 1] - prefix[i + 1 - k] >= dp[i - 1]) {
            dp[i] = prefix[i + 1] - prefix[i + 1 - k];
            left[i] = i + 1 - k;
        } else {
            dp[i] = dp[i - 1];
            left[i] = left[i - 1];
        }
    }

    right[n - k] = n - k;
    for (int i = n - k - 1; i >= 0; --i) {
        if (prefix[i + k] - prefix[i] >= prefix[right[i + 1] + k] - prefix[right[i + 1]]) {
            right[i] = i;
        } else {
            right[i] = right[i + 1];
        }
    }

    vector<int> result(3);
    int maxSum = 0;
    for (int i = k; i <= n - 2 * k; ++i) {
        int l = left[i - 1];
        int r = right[i + k];
        int totalSum = (prefix[i + k] - prefix[i]) + (prefix[l + k] - prefix[l]) + (prefix[r + k] - prefix[r]);
        if (totalSum > maxSum) {
            maxSum = totalSum;
            result = {l, i, r};
        }
    }

    return result;
}

int main() {
    vector<int> nums = {1, 2, 1, 2, 6, 7, 5, 1};
    int k = 2;
    vector<int> result = maxSumOfThreeSubarraysDP(nums, k);
    for (int i : result) {
        cout << i << " ";
    }
    return 0;
}