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: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
)

type Diff struct {
	Num int
}

type Diffs []Diff

func (d Diffs) Len() int {
	return len(d)
}

func (d Diffs) Swap(i, j int) {
	d[i], d[j] = d[j], d[i]
}

func (d Diffs) Less(i, j int) bool {
	return d[i].Num > d[j].Num
}

var (
	sc = bufio.NewScanner(os.Stdin)
	mod int = 1e9 + 7
)

func init() {
	sc.Split(bufio.ScanWords)
}

func main() {
	N := getInt()
	M := getInt()

	sum := 0
	var diffs Diffs
	for i := 0; i < N; i++ {
		input := getInt()
		sum += input

		for i := 0; i < M; i++ {
			before := input / pow(2, i)
			after := input / pow(2, i+1)
			diff := before - after
			
			if diff != 0 {
				diffs = append(diffs, Diff{Num: diff})
			}
		}
	}

	sort.Sort(diffs)

	diffSum := 0
	for i := 0; i < M; i++ {
		diffSum += diffs[i].Num
	}

	fmt.Println(sum - diffSum)
}

func getInt() int {
	sc.Scan()
	str := sc.Text()
	value, _ := strconv.Atoi(str)
	return value
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

func abs(a int) int {
	return int(math.Abs(float64(a)))
}

func pow(p, q int) int {
	return int(math.Pow(float64(p), float64(q)))
}

func min(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func max(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func strSearch(a []string, b string) bool {
	for i := 0; i < len(a); i++ {
		if a[i] == b {
			return true
		}
	}
	return false
}

func printIntArray(array []int) {
	strArray := fmt.Sprint(array)
	fmt.Println(strArray[1 : len(strArray) - 1])
}

func calcMod(x int) int {
	return x % mod
}