1508 - Range Sum of Sorted Subarray Sums.

Medium

You are given the array nums consisting of n positive integers. You computed the sum of all non-empty continuous subarrays from the array and then sorted them in non-decreasing order, creating a new array of n * (n + 1) / 2 numbers.

Return the sum of the numbers from index left to index right ( indexed from 1 ), inclusive, in the new array. Since the answer can be a huge number return it modulo <code>10⁹ + 7</code>.

Example 1:

Input: nums = 1,2,3,4, n = 4, left = 1, right = 5

Output: 13

Explanation: All subarray sums are 1, 3, 6, 10, 2, 5, 9, 3, 7, 4. After sorting them in non-decreasing order we have the new array 1, 2, 3, 3, 4, 5, 6, 7, 9, 10. The sum of the numbers from index le = 1 to ri = 5 is 1 + 2 + 3 + 3 + 4 = 13.

Example 2:

Input: nums = 1,2,3,4, n = 4, left = 3, right = 4

Output: 6

Explanation: The given array is the same as example 1. We have the new array 1, 2, 3, 3, 4, 5, 6, 7, 9, 10. The sum of the numbers from index le = 3 to ri = 4 is 3 + 3 = 6.

Example 3:

Input: nums = 1,2,3,4, n = 4, left = 1, right = 10

Output: 50

Constraints:

• n == nums.length

• 1 <= nums.length <= 1000

• 1 <= nums[i] <= 100

• 1 <= left <= right <= n * (n + 1) / 2