Solution: Range Sum of Sorted Subarray Sums

Explore how to calculate the sum of elements in a sorted array of subarray sums from a given range using binary search and sliding window methods. Understand the optimization over brute-force approaches and learn to handle large inputs efficiently by leveraging sorting, counting, and sum calculation techniques.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given an integer array nums containing $n$ positive integers along with left and right. Calculate the sum of its elements for every non-empty continuous subarray of nums. Collect these sums into a new array and sort it in nondecreasing order. This will result in a new array of size $n \times (n + 1) /2$ .

Your task is to return the sum of the elements in this sorted array from the index left to right (inclusive with 1-based indexing).

Note: As the result can be large, return the sum modulo $10^9 + 7$ .

Constraints:

$n =$ nums.length
$1 \leq$ nums.length $\leq 1000$
$1 \leq$ nums[i] ...