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 PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php
 
$a = explode(' ', trim(fgets(STDIN)));
$numbers = explode(' ', trim(fgets(STDIN)));
 
$n = $a[0];
$m = $a[1];
 
$heap = new SplPriorityQueue();
 
foreach ($numbers as $n) {
    $heap->insert((int)$n);
}
 
for ($i = 0; $i < $m; $i++) {
    $max = floor($heap->extract() / 2);
    $heap->insert($max);
}
 
$ans = [];
while ($heap->valid()) {
    $ans[] = $heap->extract();
}
 
echo array_sum($ans);