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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int M = int.Parse(input[1]);
            List<int> A = new List<int>();
            string[] input2 = Console.ReadLine().Split(' ');
            for (var i = 0; i < N; i++)
            {
                A.Add(int.Parse(input2[i]));
            }
            A.Sort();
            int c = M;
            if (N == 1)
            {
                for (var i = 0; i < M; i++)
                {
                    A[0] /= 2;
                }
            }
            else
            {
                while (c > 0)
                {
                    int max = A[N - 1] / 2;
                    for (var i = N-1; i >= 0; i--)
                    {
                        if (A[i] >= max)
                        {
                            A[i] /= 2;
                            c--;
                            if (c == 0) break;
                        }
                        else
                        {
                            if (A[i] > A[i+1])
                            {
                                A.Sort();
                            }
                            break;
                        }
                    }
                }
            }
            long ans = 0;
            for (var i = 0; i < N; i++)
            {
                ans += A[i];
            }
            Console.WriteLine(ans);
        }
    }
}