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Solution: Range Sum of Sorted Subarray Sums

Explore an optimized approach to find the sum of elements from a sorted array of subarray sums within a specified range. This lesson helps you understand how to apply binary search combined with a sliding window technique to efficiently calculate cumulative sums without explicitly generating all subarray sums. You will learn to pinpoint sum thresholds and evaluate subarray counts, gaining skills to solve complex sorting and searching problems with improved time complexity.

Statement

You are given an integer array nums containing nn 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×(n+1)/2n \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 ...