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;
using System.Collections.Generic;

namespace D
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] nm = Console.ReadLine().Split().Select(int.Parse).ToArray();

            int n= nm[0];
            int m = nm[1];
            
            List <double> a =Console.ReadLine().Split().Select(double.Parse).ToList();

            a = a.OrderBy(i => Guid.NewGuid()).ToList();
            a = a.OrderByDescending(x => x).ToList();

            int aP = 0;


            while(m > 0)
            {
                a[aP] = useDiscount(a[aP]);
                m--;
                
                double preMax = a[aP];
                
                // a.RemoveAt(0);

                int index = 0;
                int AC = a.Count();

                while(index < AC && preMax <= a[index])
                {
                    index++;
                }
                aP = index;
                // a.Insert(index, preMax);

            }

            for(int i=0;i<a.Count();i++)
            {
                a[i] = (double)(int) a[i];
            }
            

            Console.WriteLine(a.Sum());
        }

        public static double useDiscount(double x)
        {
            return (double)(x / 2.0);
        }
    }
}