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;

namespace abc141_d
{
    static class Program
    {
        static void Main(string[] args)
        {
            var items = Console.ReadLine().ToIntArray();
            // 商品数
            var n = items[0];
            // 割引券数
            var m = items[1];
            // 買った商品の値段一覧
            var a = Console.ReadLine().ToIntArray();

            var sum = 0L;
            for (int i = 0; i < a.Length; i++)
            {
                sum += a[i];
            }

            Array.Sort(a);

            var last = n - 1;
            for (var i = 0; i < m; i++)
            {
                var value = a[last];
                a[last] /= 2;
                sum = sum - value + a[last];
                if (last > 0 && a[last] < a[last - 1])
                {
                    Array.Sort(a);
                }
                if (a[last] <= 0)
                {
                    break;
                }
            }

            //var sum = 0L;
            //for (int i = 0; i < a.Length; i++)
            //{
            //    sum += a[i];
            //}
            Console.WriteLine($"{sum}");
        }

        static int ToInteger(this string s)
        {
            return int.Parse(s);
        }

        static int[] ToIntArray(this string s, char separator = ' ')
        {
            return s.Split(separator).Select(m => m.ToInteger()).ToArray();
        }
    }
}