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

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] stdR1 = br.readLine().split(" ");
        int N = Integer.parseInt(stdR1[0]);
        int M = Integer.parseInt(stdR1[1]);
        
        String[] stdR2 = br.readLine().split(" ");
        PowerfulDiscountTickets pdt = new PowerfulDiscountTickets(N, M);
        
        for(int i = 0; i < N; i++){
            pdt.goods[i] = Integer.parseInt(stdR2[i]);
        }
        
        System.out.println(pdt.binarySearch());
    }
}

class PowerfulDiscountTickets{
    int N;
    int M;
    int[] goods;
    
    public PowerfulDiscountTickets(int N, int M){
        this.N = N;
        this.M = M;
        goods = new int[N];
    }
    
    public long binarySearch(){
        long left = -1;
        long right = 100_000_000_000_000L;
        
        while(right - left > 1){
            long mid = (left + right) / 2;
            if(isOK(mid)){
                right = mid;
            }else{
                left = mid;
            }
        }
        
        return right;
    }
    
    private boolean isOK(long price){
        
        int[] goods2 = goods.clone();
        Arrays.sort(goods2);
        
        long sum = 0;
        for(int i = 0; i < N; i++){
            sum += goods2[i];
        }
        
        for(int i = 0; i < M; i++){
            int before = goods2[N-1];
            goods2[N-1] /= 2;
            sum = sum - before + goods2[N-1];
            if( sum <= price ) break;
            Arrays.sort(goods2);
        }
        
        return sum <= price;
    }
    

}