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: Time Limit Exceeded)

namespace ABC141.D
{
    using System.Collections.Generic;
    using System.Linq;
    using static System.Console;

    public class Program
    {

        public static void Main(string[] args)
        {
            var l = ReadInputsAsLong().ToList();
            var n = l[0];
            var m = l[1];

            WriteLine(Solve(m,
                ReadInputsAsLong().ToList()
                ));
        }

        /// <summary>
        /// 
        /// </summary>
        /// <param name="m">割引券の枚数</param>
        /// <param name="a">i番目の商品の値段</param>
        public static long Solve(long m, List<long> a)
        /// <returns></returns>
        {
            SortedList<long, long> pricesAndCounts = new SortedList<long, long>();

            for (int i = 0; i < a.Count(); i++)
            {
                if (pricesAndCounts.ContainsKey(a[i]))
                {
                    pricesAndCounts[a[i]] += 1;
                    continue;
                }
                pricesAndCounts.Add(a[i], 1);
            }

            for (long i = 0; i < m; i++)
            {
                long maxval = pricesAndCounts.Keys.Last();
                pricesAndCounts[maxval] -= 1;

                var k = maxval / 2;
                if (pricesAndCounts.ContainsKey(k))
                {
                    pricesAndCounts[k] += 1;
                }
                else
                {
                    pricesAndCounts.Add(k, 1);
                }

                if (pricesAndCounts[maxval] == 0) pricesAndCounts.RemoveAt(pricesAndCounts.Count - 1);
            }

            return pricesAndCounts.Select(kv => kv.Key * kv.Value).Sum();
        }

        static IEnumerable<long> ReadInputsAsLong() => ReadLine().Split(' ').Select(x => long.Parse(x));

    }
}