You have an `inventory`

of different colored balls, and there is a customer that wants `orders`

balls of **any** color.

The customer weirdly values the colored balls. Each colored ball's value is the number of balls **of that color **you currently have in your `inventory`

. For example, if you own `6`

yellow balls, the customer would pay `6`

for the first yellow ball. After the transaction, there are only `5`

yellow balls left, so the next yellow ball is then valued at `5`

(i.e., the value of the balls decreases as you sell more to the customer).

You are given an integer array, `inventory`

, where `inventory[i]`

represents the number of balls of the `i`

color that you initially own. You are also given an integer ^{th}`orders`

, which represents the total number of balls that the customer wants. You can sell the balls **in any order**.

Return *the maximum total value that you can attain after selling *

`orders`

`10`^{9 }+ 7

.

**Example 1:**

Input:inventory = [2,5], orders = 4Output:14Explanation:Sell the 1st color 1 time (2) and the 2nd color 3 times (5 + 4 + 3). The maximum total value is 2 + 5 + 4 + 3 = 14.

**Example 2:**

Input:inventory = [3,5], orders = 6Output:19Explanation:Sell the 1st color 2 times (3 + 2) and the 2nd color 4 times (5 + 4 + 3 + 2). The maximum total value is 3 + 2 + 5 + 4 + 3 + 2 = 19.

**Example 3:**

Input:inventory = [2,8,4,10,6], orders = 20Output:110

**Example 4:**

Input:inventory = [1000000000], orders = 1000000000Output:21Explanation:Sell the 1st color 1000000000 times for a total value of 500000000500000000. 500000000500000000 modulo 10^{9 }+ 7 = 21.

**Constraints:**

`1 <= inventory.length <= 10`

^{5}`1 <= inventory[i] <= 10`

^{9}`1 <= orders <= min(sum(inventory[i]), 10`

^{9})

class Solution {
public:
int maxProfit(vector<int>& inventory, int orders) {
}
};