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)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0].split(" ")[0]);
    const M = parseInt(arg[0].split(" ")[1]);
    
    const A = arg[1].split(" ").map(n=>parseInt(n)).sort((a,b)=>a-b);
    
    
    for(let i=0; i<M; i++) {
        const highest = A[A.length - 1];
        const halfed   = Math.floor(highest / 2);
        
        A.pop();
        
        for(let j=A.length; j>=0; j--) {
            if(A[j] < halfed) {
                A.splice(j+1, 0, halfed);
                break;
            }
            
            if(j === 0) {
                A.unshift(halfed);
            }
        }
    }

    console.log(A.reduce((m,n)=>m+n));
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));