Calculate Revenue from Highest-Inventory VM Sales

A provider sells units from several VM inventory types. The price of one unit equals that type's current remaining inventory immediately before the sale. Each customer buys one unit from a type with the greatest current inventory, then that type's inventory decreases by one.

Function Signature

vm_revenue(inventory: list[int], customers: int) -> int

Output

Return total revenue after serving exactly customers customers. Any type tied for greatest inventory may be chosen; the total revenue is unchanged by that tie choice. Types with zero inventory cannot be sold.

Constraints

• 1 <= len(inventory) <= 200000.
• 0 <= inventory[i] <= 1000000000.
• 0 <= customers <= 200000.
• customers <= sum(inventory).
• Use an integer type large enough for the total revenue, which may exceed a signed 32-bit integer.
• Do not mutate the input array.

Examples

Input: inventory = [1,2,4], customers = 4

Output: 11

The four sale prices are 4, 3, 2, and 2.

Input: inventory = [2,2], customers = 3

Output: 5

Input: inventory = [0,3], customers = 0

Output: 0