Powerful Discount Tickets

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.

Examples

Input

3 3 2 13 8

Output

9

Input

4 4 1 9 3 5

Output

6

Input

1 100000 1000000000

Output

0

Input

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

Output

9500000000

inputFormat

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

outputFormat

Output

Print the minimum amount of money required to buy all the items.

Examples

Input

3 3 2 13 8

Output

9

Input

4 4 1 9 3 5

Output

6

Input

1 100000 1000000000

Output

0

Input

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

Output

9500000000

样例

1 100000
1000000000

0