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 Lua (5.3.2) (judge verdict: Wrong Answer)

n,m=io.read("*n","*n","*l")
a={}
for i=1,n do
    a[i]=io.read("*n")
end
table.sort(a)
if n==1 then
    return print(string.format("%d",a[1]//(2^m)))
end

t={}
key=n
for i=1,m do
    a[key]=a[key]//2
    table.insert(t,{a[key],key})
    if #t>1 then
        table.sort(t,function(a,b)
            return a[1]<b[1]
        end)
    end
    if t[#t][1]<=a[key] then
        key=t[#t][2]
    else
        if key-1==0 then
            break
        else
            key=key-1
        end
    end
end

total=0
for i=1,n do
    total=total+a[i]
end
print(total)