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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main extends App {

  val inputnm = scala.io.StdIn.readLine()
  val nmArray = inputnm.split(" ").map(_.toInt).toVector
  val inputa = scala.io.StdIn.readLine()

  val n = nmArray(0)
  val m = nmArray(1)
  var aArray = inputa.split(" ").map(_.toLong).toVector

  (1 to m).foreach { _ =>
    if (aArray.size > 0) {
      val max = aArray.max
      aArray = aArray.updated(aArray.indexWhere(_ == max), max / 2L).filter(_ > 0)
    }
  }

  println(aArray.sum)

}