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: Accepted)

import java.util.PriorityQueue
import kotlin.comparisons.compareByDescending
fun main(args: Array<String>) {
    var (N, M) = listOfInt()
    val A = listOfLong()
    val Q = PriorityQueue<Long>(N, compareByDescending { it })
    A.forEach { Q.add(it) }
    repeat (M) {
        val e = Q.poll()!!
        Q.add(e / 2)
    }
    var ans = 0L
    while (Q.size > 0) {
        ans += Q.poll()!!
    }
    println(ans)
}
fun next() = readLine()!!
fun listOfString() = next().split(" ")
fun listOfInt(delta: Int = 0) = listOfString().map { Integer.parseInt(it) + delta }
fun listOfLong(delta: Long = 0L) = listOfString().map { java.lang.Long.parseLong(it) + delta }