Maximum Supplier Profit

You are given an array arr of N positive integers, where arr[i] represents the number of products available from the i-th supplier. You are also given a positive integer M, which is the total number of products you must sell.

The profit gained from selling a single product from a supplier is equal to the number of products that supplier currently has. Each time you sell a product from a supplier, their count of available products decreases by one.

Your task is to find the maximum possible profit you can achieve by selling exactly M products.

Input Format:

The first line contains two space-separated integers, N (the number of suppliers) and M (the number of products to sell).

The second line contains N space-separated integers, representing the elements of the arr array.

Output Format:

Print a single integer representing the maximum possible profit.

Note:

To maximize profit at any given step, it is always optimal to sell from the supplier who currently has the most products. A simple simulation of selling one product at a time might be too slow if M is large. A more efficient approach involves sorting the suppliers and selling products in "layers" from the top suppliers. The total profit can be very large, so be sure to use a 64-bit integer type (like long in Java or long long in C++) for your calculations.