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})

```
struct Solution;
const MOD: i64 = 1_000_000_007;
impl Solution {
fn max_profit(mut inventory: Vec<i32>, mut orders: i32) -> i32 {
let n = inventory.len();
inventory.sort_unstable();
let mut res: i64 = 0;
for i in (0..n).rev() {
let diff = if i > 0 {
inventory[i] - inventory[i - 1]
} else {
inventory[i]
};
let w = (n - i) as i32;
if orders >= diff * w {
res += (inventory[i] - diff + 1 + inventory[i]) as i64 * diff as i64 / 2 * w as i64;
res %= MOD;
orders -= diff * w;
} else {
let diff = orders / w;
res += (inventory[i] - diff + 1 + inventory[i]) as i64 * diff as i64 / 2 * w as i64;
res %= MOD;
orders -= diff * w;
let h = inventory[i] - diff;
while orders > 0 {
res += h as i64;
res %= MOD;
orders -= 1;
}
break;
}
}
res as i32
}
}
#[test]
fn test() {
let inventory = vec![2, 5];
let orders = 4;
let res = 14;
assert_eq!(Solution::max_profit(inventory, orders), res);
let inventory = vec![3, 5];
let orders = 6;
let res = 19;
assert_eq!(Solution::max_profit(inventory, orders), res);
let inventory = vec![2, 8, 4, 10, 6];
let orders = 20;
let res = 110;
assert_eq!(Solution::max_profit(inventory, orders), res);
let inventory = vec![2, 8, 4, 10, 6];
let orders = 20;
let res = 110;
assert_eq!(Solution::max_profit(inventory, orders), res);
let inventory = vec![1000000000];
let orders = 1000000000;
let res = 21;
assert_eq!(Solution::max_profit(inventory, orders), res);
}
```