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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.math.BigInteger

fun main(args: Array<String>){
  var input = readLine()!!.split(" ")
  val N = input[0].toInt()
  val M = input[1].toInt()
  input = readLine()!!.split(" ")
  val A = Array(N){ input[it].toInt() }
  A.sortBy{ -it }

  var i = 0
  for( m in 1..M ){
    A[i] /= 2
    if( i == N-1 )
      i = 0
    else if( A[i] < A[i+1] )
      i++
    if( A[i] <= A[0] )
      i = 0
  }

  var all = BigInteger.ZERO
  for( a in A )
    all = all.plus(BigInteger(a.toString()))
  println(all)
}