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: Wrong Answer)

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

class Program
{
    //static int[] dp;
    //static decimal[,,] dp;
    //static decimal N;
    static void Main(string[] args)
    {
        // 入力
        int[] input = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();
        int N = input[0];
        int M = input[1];
        input = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();
        List<int> cost = new List<int>(input);
        cost.Sort((a, b) => (b - a));

        // 一番値段の高いものに割引券を使う
        for (int i = 0; i < M; i++)
        {
            PK(ref cost); // 要素0番目を適切な位置にする
        }

        // 割引券を全部使った
        long check = 0;
        for (int i = 0; i < N; i++)
        {
            check += cost[i];
        }

        Console.WriteLine(check + "");
    }

    private static void PK(ref List<int> cost)
    {
        cost[0] = cost[0] / 2;
        // 要素0をいい感じにする
        // 末端に行くまでしたと入れ替えていく
        // i*2 + 1番目と i*2+2番目とくらべる
        int len = cost.Count;
        int i = 0;
        while (true)
        {
            //左下と比較
            if((i*2+1) < len && cost[i] < cost[i*2+1])
            {
                int tmp = cost[i];
                cost[i] = cost[i * 2 + 1];
                cost[i * 2 + 1] = tmp;
            }
            else if((i * 2 + 2) < len && cost[i] < cost[i*2+2])
            {
                int tmp = cost[i];
                cost[i] = cost[i * 2 + 2];
                cost[i * 2 + 2] = tmp;
            }
            else
            {
                break;
            }
        }
    }


}