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: Accepted)

using System;
using System.Numerics;
using System.Linq;
using System.Collections.Generic;
using System.Text;

namespace debug
{
    class ProgramD
    {
        static void Main(string[] args)
        {

            //入力
            string[] s1  = Console.ReadLine().Split(' ');
            int n = int.Parse(s1[0]);
            int m = int.Parse(s1[1]);

            string[] s2 = Console.ReadLine().Split(' ');
           

            var q = new PriorityQueue<int>(n);
            for (int i = 0; i < n; i++)
                q.Enqueue(int.Parse(s2[i]));


            for (int i = 0; i < m; i++)
            {
                int temp = q.Dequeue();
                temp /= 2;
                q.Enqueue(temp);
            }

            long sum = 0;

            for (int i = 0; i < n; i++)
                sum += q.Dequeue();
            

            Console.WriteLine(sum);

        }

        
    }

    /*優先度付きキュー*/
    class PriorityQueue<T> where T : IComparable<T>
    {
        public readonly T[] Array;
        public readonly bool Greater;
        public int Count { get; private set; } = 0;

        public PriorityQueue(int capacity, bool greater = true)
        {
            this.Array = new T[capacity];
            this.Greater = greater;
        }

        public void Enqueue(T item)
        {
            this.Array[this.Count] = item;
            this.Count += 1;
            this.UpHeap();
        }

        public T Dequeue()
        {
            // 先頭要素を末尾にして再構成
            this.Swap(0, this.Count - 1);
            this.Count -= 1;
            this.DownHeap();

            return this.Array[this.Count];
        }


        private void UpHeap()
        {
            var n = this.Count - 1;
            while (n != 0)
            {
                // 親要素の座標
                var parent = (n - 1) / 2;

                if (this.Compare(this.Array[n], this.Array[parent]) > 0)
                {
                    this.Swap(n, parent);
                    n = parent;
                }
                else
                {
                    break;
                }
            }
        }

        private void DownHeap()
        {
            var parent = 0;
            while (true)
            {
                var child = 2 * parent + 1;
                if (child > this.Count - 1) break;

                if (child < this.Count - 1 && this.Compare(this.Array[child], this.Array[child + 1]) < 0)
                {
                    // 左より右の子のほうが大きい値の場合、右を入れ替え対象にする
                    child += 1;
                }

                if (this.Compare(this.Array[parent], this.Array[child]) < 0)
                {
                    this.Swap(parent, child);
                    parent = child;
                }
                else
                {
                    break;
                }
            }
        }

        //aとbを比較する
        private int Compare(T a, T b)
        {
            var c = a.CompareTo(b);
            if (!this.Greater)
            {
                c = -c;
            }
            return c;
        }

        //aとbを入れ替える
        private void Swap(int a, int b)
        {
            var tmp = this.Array[a];
            this.Array[a] = this.Array[b];
            this.Array[b] = tmp;
        }
    }

}