Powerful Discount Tickets

AtCoder

IDabc141_d

Time2000ms

Memory256MB

Difficulty—

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: $N$ $M$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

3 3
2 13 8

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.

Input #2

4 4
1 9 3 5

Output #2

Input #3

1 100000
1000000000

Output #3

0

We can buy the item priced $1000000000$ yen for $0$ yen with $100000$ tickets.

Input #4

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

Output #4

9500000000

API Response (JSON)

{
  "problem": {
    "name": "Powerful Discount Tickets",
    "description": {
      "content": "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 a",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc141_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is going to buy $N$ items one by one.\nThe price of the $i$\\-th item he buys is $A_i$ yen (the currency of Japan).\nHe has $M$ discount tickets, and he can use any number of them when buying a...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments