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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}

class Main{
    public static void main(String[] args){ new Main().solve();}
    
    static FastScanner scan = new FastScanner();
    static final int MOD = 1_000_000_007;
    static final int INF = 2147483647;
    static final long LINF = 9223372036854775807L;

    // Scanner
    int ni(){return scan.nextInt();}
    int[] ni(int n){int[] a = new int[n]; for(int i = 0; i < n; i++){a[i] = ni();} return a;}
    int[][] ni(int y, int x){int[][] a = new int[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ni();}} return a;}
    long nl(){return scan.nextLong();}
    long[] nl(int n){long[] a = new long[n]; for(int i = 0; i < n; i++){a[i] = nl();} return a;}
    long[][] nl(int y, int x){long[][] a = new long[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = nl();}} return a;}
    String ns(){return scan.next();}
    String[] ns(int n){String[] a = new String[n]; for(int i = 0; i < n; i++){a[i] = ns();} return a;}
    String[][] ns(int y, int x){String[][] a = new String[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ns();}} return a;}

    // Math
    int max(int a, int b){return Math.max(a, b);}
    long max(long a, long b){return Math.max(a, b);}
    double max(double a, double b){return Math.max(a, b);}
    int max(int[] a){int max = a[0]; for(int value:a){max = max(max,value);} return max;}
    long max(long[] a){long max = a[0]; for(long value:a){max = max(max,value);} return max;}
    double max(double[] a){double max = a[0]; for(double value:a){max = max(max,value);} return max;}
    int min(int a, int b){return Math.min(a, b);}
    long min(long a, long b){return Math.min(a, b);}
    double min(double a, double b){return Math.min(a, b);}
    int min(int[] a){int min = a[0]; for(int value:a){min = min(min,value);} return min;}
    long min(long[] a){long min = a[0]; for(long value:a){min = min(min,value);} return min;}
    double min(double[] a){double min = a[0]; for(double value:a){min = min(min,value);} return min;}
    long sum(int[] a){long sum = 0; for(int value:a){sum += value;} return sum;}
    long sum(long[] a){long sum = 0; for(long value:a){sum += value;} return sum;}
    double sum(double[] a){double sum = 0; for(double value:a){sum += value;} return sum;}
    int gcd(int a, int b){return b == 0 ? a : gcd(b, a % b);}
    long gcd(long a, long b){return b == 0 ? a : gcd(b, a % b);}
    int lcm(int a, int b){return a / gcd(a, b) * b;}
    long lcm(long a, long b){return a / gcd(a, b) * b;}

    // Array
    void sort(int[] a){ Arrays.sort(a);}
    void sort(long[] a){ Arrays.sort(a);}
    void sort(double[] a){ Arrays.sort(a);}
    void sort(String[] a){ Arrays.sort(a);}
    int[] reverse(int[] a){
        int[] reversed = new int[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    long[] reverse(long[] a){
        long[] reversed = new long[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    double[] reverse(double[] a){
        double[] reversed = new double[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    String[] reverse(String[] a){
        String[] reversed = new String[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    boolean[] reverse(boolean[] a){
        boolean[] reversed = new boolean[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    void fill(int[] array, int x) { Arrays.fill(array, x); }
    void fill(long[] array, long x) { Arrays.fill(array, x); }
    void fill(double[] array, double x) { Arrays.fill(array, x); }
    void fill(boolean[] array, boolean x) { Arrays.fill(array, x); }
    void fill(int[][] array, int x) { for(int a[] : array) { fill(a, x); } }
    void fill(long[][] array, long x) { for(long a[] : array) { fill(a, x); } }
    void fill(double[][] array, double x) { for(double a[] : array) { fill(a, x); } }
    void fill(boolean[][] array, boolean x) { for(boolean a[] : array) { fill(a, x); } }



    public void solve(){
        int n = ni();
        int m = ni();
        long[] a = nl(n);

        while(m > 0){
            sort(a);
            a[n-1] /= 2;
            m--;
        }

        System.out.println(sum(a));
        
    }
}