Arrange Values to Maximize Range Requests

### Problem Rearrange the values of `nums` before answering all inclusive, zero-based ranges in `requests`. Each request contributes the sum of the values in its range. Return the largest possible combined sum, reduced modulo `10^9 + 7`. ```cpp class Solution { public: int maxSumRangeQuery(vector<int>& nums, vector<vector<int>>& requests); }; ``` ### Examples **Example 1:** ```text nums = [2,4,6], requests = [[0,1],[1,2]] Output: 18 Explanation: Put 6 in the middle; its contribution is doubled, giving 2 + 12 + 4. ``` **Example 2:** ```text nums = [0,5,8], requests = [[0,0],[0,0]] Output: 16 Explanation: Put 8 at position 0 for both requests. ``` ### Constraints - `n == nums.length` and `1 <= n <= 10^5`. - `0 <= nums[i] <= 10^5`. - There are `1..10^5` requests, each with two endpoints satisfying `0 <= start <= end < n`. ### Clarifying Questions Choose one common permutation for all requests. The result is the optimum sum, rather than the permutation that achieves it. ```hint Inspect the structure How does one chosen rearrangement affect repeated or overlapping requests? ``` ### Reasoning checkpoints - Evaluate one common rearrangement across all requests, including repeated and overlapping ranges. - Prove that no other rearrangement has a larger combined sum, and apply the modulus without changing the optimization. ### Optional extensions How would signed values affect the same rearrangement argument?