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 (Lua 5.3.5) (judge verdict: Accepted)

local function meld(a,b)
    if not a then
        return b
    elseif not b then
        return a
    elseif a[1]<b[1] then
        b[4]=a[3]
        a[3]=b
        return a
    else
        a[4]=b[3]
        b[3]=a
        return b
    end
end

local function pair(a,d)
    local b=a and a[4]
    if b then
        local c=b[4]
        a=meld(a,b)
        a[4]=d
        d=a
        return pair(c,d)
    else
        local e
        while d do
            e=d
            d=d[4]
            a=meld(a,e)
        end
        return a
    end
end

local PairingHeap={}

PairingHeap.empty=function(self)
    return not self[1]
end

PairingHeap.push=function(self,key,value)
    self[1]=meld(self[1],{key,value,false,false})
end

PairingHeap.top=function(self)
    return self[1][2]
end

PairingHeap.pop=function(self)
    self[1]=pair(self[1][3],false)
end

PairingHeap.join=function(self,other)
    self[1]=meld(self[1],other[1])
    return self
end

PairingHeap.new=function(self)
    local obj={false}
    setmetatable(obj,{__index=PairingHeap})
    return obj
end

----------

local n,m=io.read("n","n")
local a=PairingHeap:new()
for i=1,n do
    local input=io.read("n")
    a:push(-input,input)
end

for i=1,m do
    local x=a:top()
    x=(x//2)
    a:pop()
    a:push(-x,x)
end
 
local total=0
for i=1,n do
    total=total+a:top()
    a:pop()
end
print(total)