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)

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];

            Heap pq = new Heap(Console.ReadLine().Split().Select(long.Parse).ToList());


            while (m > 0)
            {
                long A = (int)pq.Pop() >> 1;
                pq.Push(A);
                // pq.Push((int)pq.Pop() >> 1);
                m--;
            }

            long sum = 0;
            while (pq.q.Count() > 0)
            {
                sum += (long)pq.Pop();
            }

            Console.WriteLine(sum);

        }

        public class Heap
        {
            public List<long> q;

            public Heap(List<long> Array)
            {
                q = new List<long>();
                foreach (var x in Array) this.Push(x);
            }

            public void Push(long elem)
            {
                int n = q.Count();
                q.Add(elem);

                while (n != 0)
                {
                    //親
                    int i = (n - 1) / 2;
                    if (q[n] > q[i])
                    {
                        var tmp = q[n];
                        q[n] = q[i];
                        q[i] = tmp;
                    }
                    n = i;
                }
            }

            public long Pop()
            {
                long ret = q.First();
                q[0] = q.Last();
                q.RemoveAt(q.Count() - 1);

                for (int i = 0; i * 2 + 1 < q.Count();)
                {
                    int A = 0;

                    if (i * 2 + 2 >= q.Count())
                    {
                        if (i * 2 + 2 > q.Count())
                        {
                            break;
                        }
                        else
                        {
                            long L = q[i];
                            long R = q[i * 2 + 1];

                            if (L == R)
                            {
                                break;
                            }
                            if(L > R)
                            {
                                break;
                            }
                            A = i * 2 + 1;

                        }

                    }
                    else
                    {
                        long L = q[i * 2 + 1];
                        long R = q[i * 2 + 2];

                        if (L == q[i] || R == q[i])
                        {
                            break;
                        }
                        if (q[i] < L || q[i] < R)
                        {
                            A = L > R ? i * 2 + 1 : i * 2 + 2;
                        }
                    }

                    long tmp = q[i];
                    q[i] = q[A];
                    q[A] = tmp;
                    i = A;
                }

                return ret;
            }

        }


    }

}