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-----
3 3
2 13 8

-----Sample Output-----
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.

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