Range Sum of Sorted Subarray Sums

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] $\leq 100$

• $1 \leq$ left $\leq$ right $\leq n \times (n + 1) / 2$

Examples