Contest Duration: ~ (local time) (300 minutes) Back to Home
H - Powerful Discount Tickets /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

i 番目に買う品物の値段は A_i 円です。

X 円の品物を買う際に Y 枚の割引券を使った場合、その品物を \frac{X}{2^Y} 円(小数点以下切り捨て)で買うことができます。

### 制約

• 入力は全て整数である。
• 1 \leq N, M \leq 10^5
• 1 \leq A_i \leq 10^9

### 入力

N M
A_1 A_2 ... A_N


### 入力例 1

3 3
2 13 8


### 出力例 1

9


• 1 番目に買う品物には割引券を使わず、2 円で買います。
• 2 番目に買う品物には 2 枚の割引券を使い、3 円で買います。
• 3 番目に買う品物には 1 枚の割引券を使い、4 円で買います。

### 入力例 2

4 4
1 9 3 5


### 出力例 2

6


### 入力例 3

1 100000
1000000000


### 出力例 3

0


1000000000 円の品物を買う際に 100000 枚の割引券を使うと 0 円で買うことができます。

### 入力例 4

10 1
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000


### 出力例 4

9500000000


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