You are given an integer array nums representing the strength of various heroes.

The power of a nonempty group of heroes is defined as the product of the square of the maximum strength in the group and the minimum strength in the group. Specifically, for a group with maximum value $M$ and minimum value $m$, its power is $M^2 imes m$.

Return the sum of the powers of all nonempty groups of heroes. Since the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

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.