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.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
            // 入力
            string[] sS = System.Console.ReadLine().Trim().Split(' ');
            int iN = int.Parse(sS[0]);                                                              // 個数
            int iM = int.Parse(sS[1]);                                                              // 枚数
            List<decimal> lstA = new List<decimal>();
            sS = System.Console.ReadLine().Trim().Split(' ');
            for (int i = 0; i < sS.Length; i++) { lstA.Add(decimal.Parse(sS[i])); }                 // 各価格

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            for (int i = 0; i < iM; i++)
            {
                //lstA.Sort(delegate (decimal mca1, decimal mca2) { return (int)(mca2 - mca1); });    // 降順
                lstA.Sort();                                                                        // 昇順
                lstA.Reverse();                                                                     // 降順
                lstA[0] = lstA[0] / 2M;
                //DispDebug(lstA);
            }
            for (int i = 0; i < lstA.Count; i++)
            {
                lstA[i] = Math.Truncate(lstA[i]);
            }
            //DispDebug(lstA);

            // 出力
            System.Console.WriteLine("{0}", lstA.Sum().ToString().Trim());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }

        // debug
        private static void DispDebug(List<decimal> lstA)
        {
            StringBuilder sbS = new StringBuilder();
            for (int i = 0; i < lstA.Count; i++)
            {
                sbS.Append(lstA[i].ToString("0.00000000") + "  ");
            }
            System.Console.WriteLine("{0}", sbS.ToString().Trim());
        }

}