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: Runtime Error)

using System;
using System.Linq;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{      
        var input1 = Console.ReadLine();
        var N = int.Parse(input1.Split(' ')[0]);
        var M = int.Parse(input1.Split(' ')[1]);
       
        var input2 = Console.ReadLine().Split(' ');
        var prices = new List<Int64>();
        input2.ToList().ForEach(x=>prices.Add(Int64.Parse(x)));
 
        prices.Sort();

        var price = 0;
      	while(M > 0){
          prices[N-1] = prices[N-1] /2;
          if(prices[N-2] > prices[N-1])
          {
          	prices.Sort();
          }
          M--;
        }
      
     	Console.WriteLine(prices.Sum());
	}
}