The width of a sequence is defined as the difference between its maximum and minimum elements.

Given an integer array nums, return the sum of the widths of all non empty subsequences of nums.

Note: Since the final answer can be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.