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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var n, m int
	fmt.Scan(&n, &m)
	a := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&a[i])
	}
	// sort.Sort(sort.Reverse(sort.IntSlice(a)))

	// a[0] /= 2
	for i := 0; i < m; i++ {
		sort.Sort(sort.Reverse(sort.IntSlice(a)))
		a[0] /= 2

		// index := 0
		// loop := i + 1
		// if loop > n {
		// 	loop = n
		// }
		// for j := 0; j < loop; j++ {
		// 	if a[j] > a[index] {
		// 		index = j
		// 	}
		// }
		// a[index] /= 2
	}

	res := 0
	for i := 0; i < n; i++ {
		res += a[i]
	}
	fmt.Println(res)
}