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 Ruby (2.3.3) (judge verdict: Accepted)

class PriorityQueue
  attr_accessor :data, :size

  def initialize(array = [])
    @data = []
    array.each { |a| push(a) }
  end

  def push(element)
    current = @data.size
    while current > 0
      p_index = parent(current)
      break if @data[p_index] <= element
      @data[current] = @data[p_index]
      current = p_index
    end
    @data[current] = element
  end

  def pop
    ret = @data.first
    x = @data.last
    current = 0
    while have_child?(current)
      a_index = left_child_index(current)
      b_index = right_child_index(current)
      a_index = b_index if @data[b_index] && @data[b_index] < @data[a_index]
      break if @data[a_index] >= x
      @data[current] = @data[a_index]
      current = a_index
    end
    @data[current] = x
    @data.pop

    ret
  end

  def size
    @data.size
  end

  def front
    @data.first
  end

  def empty?
    @data.empty?
  end

  private

  def parent(num)
    (num - 1) / 2
  end

  def left_child_index(num)
    2 * num + 1
  end

  def right_child_index(num)
    2 * num + 2
  end

  def have_child?(index)
    left_child_index(index) < @data.size
  end
end

n, m = gets.split.map(&:to_i)
nums = gets.split.map(&:to_i)
pq = PriorityQueue.new(nums.map { |i| -i } )
m.times { pq.push((pq.pop / 2.0).ceil) }
puts -pq.data.inject(:+)