You are given an integer array inventory, where inventory[i] represents the initial number of balls of the $i$th color. You are also given an integer orders, representing the total number of balls to sell.

The value of each ball depends on the number of remaining balls of that color. Specifically, selling a ball of a color that currently has $k$ balls remaining yields a value of $k$, after which the count of balls of that color decreases by $1$.

Return the maximum total value that can be achieved after selling orders balls. Since the answer may be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ inventory.length $\leq 10^5$

• $1 \leq$ inventory[i] $\leq 10^9$

• $1 \leq$ orders $\leq \min(\sum$inventory[i]$, 10^9)$

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.