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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use List::Util qw(max first);

my ($N, $M) = (split(/ /o, <STDIN>));
chomp($N);
chomp($M);
my @A;
my $tot = 0;
foreach (split(/ /o, <STDIN>)) {
  chomp($_);
  push(@A, $_);
  $tot += $_;
}
foreach my $i (1..$M) {
  my $t = max(@A);
  my $idx = first { $A[$_] == $t } 0..$#A;
  my $t2 = int($t/2);
  $A[$idx] = $t2;
  $tot = $tot - $t + $t2;
}
print $tot;