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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function Main(arg) {
 
    var N = arg.split("\n")[0].split(" ")[0]-0;
    var M = arg.split("\n")[0].split(" ")[1]-0;

    var A = arg.split("\n")[1].split(" ");

    for (var i = 0; i < A.length; i++){
        A[i] = A[i] - 0;
    }

    for (var i = 0; i < M; i++){
        var max = Math.max.apply(null, A);
        var index = A.indexOf(max);

        A[index] = Math.floor(A[index] / 2);
    }

    var ans = 0;
    for (var i = 0; i < N; i++) {
        ans += A[i];
    }

    console.log(ans);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));