Problem:
Score : 400 points

Problem Statement

Takahashi is going to buy N items one by one.

The price of the i-th item he buys is A_i yen (the currency of Japan).

He has M discount tickets, and he can use any number of them when buying an item.

If Y tickets are used when buying an item priced X yen, he can get the item for \frac{X}{2^Y} (rounded down to the nearest integer) yen.

What is the minimum amount of money required to buy all the items?

Constraints

All values in input are integers.

1 \leq N, M \leq 10^5

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_N

Output

Print the minimum amount of money required to buy all the items.

Sample Input 1

3 3
2 13 8

Sample Output 1

9

We can buy all the items for 9 yen, as follows:

Buy the 1-st item for 2 yen without tickets.

Buy the 2-nd item for 3 yen with 2 tickets.

Buy the 3-rd item for 4 yen with 1 ticket.

Sample Input 2

4 4
1 9 3 5

Sample Output 2

6

Sample Input 3

1 100000
1000000000

Sample Output 3

0

We can buy the item priced 1000000000 yen for 0 yen with 100000 tickets.

Sample Input 4

10 1
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 4

9500000000

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Linq;

namespace D___Powerful_Discount_Tickets
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] temp1 = Console.ReadLine().Split(' ');
            var NumberOfItems = int.Parse(temp1[0]);
            var NumberOfTickets = int.Parse(temp1[1]);

            var Price = Console.ReadLine().Split(' ');
            int[] PriceOfItem = new int[NumberOfItems];

            for (int i = 0; i < NumberOfItems; i++)
            {
                PriceOfItem[i] = int.Parse(Price[i]);
            }

            Array.Sort(PriceOfItem);

            while (NumberOfTickets > 0)
            {
                int tempPrice = 0;
                int ItemNumber = 0;
                for (int i = 0; i < NumberOfTickets; i++)
                {
                    if (tempPrice < PriceOfItem[i])
                    {
                        tempPrice = PriceOfItem[i];
                        ItemNumber = i;
                    }
                }
                PriceOfItem[ItemNumber] = PriceOfItem[ItemNumber] / 2;
                NumberOfTickets--;
            }

            Int64 TotalCost = 0;
            foreach (int cost in PriceOfItem)
            {
                TotalCost += cost;
            }
            Console.WriteLine(TotalCost);

        }
    }
}