Bread

AtCoder

IDabc252_f

Time2000ms

Memory256MB

Difficulty—

We have a loaf of bread of length $L$, which we will cut and distribute to $N$ children. The $i$\-th child $(1\leq i\leq N)$ wants a loaf of length $A_i$. Now, Takahashi will repeat the operation below to cut the loaf into lengths $A_1, A_2, \ldots, A_N$ for the children. > Choose a loaf of length $k$ and an integer $x$ between $1$ and $k-1$ (inclusive). Cut the loaf into two loaves of length $x$ and $k-x$. > This operation incurs a cost of $k$ regardless of the value of $x$. Each child $i$ must receive a loaf of length exactly $A_i$, but it is allowed to leave some loaves undistributed. Find the minimum cost needed to distribute loaves to all children. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1\leq A_i\leq 10^9$ * $A_1+A_2+\cdots+A_N\leq L\leq 10^{15}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $L$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5 7
1 2 1 2 1

Output #1

16

Takahashi can cut the loaf for the children as follows.

*   Choose the loaf of length $7$ and $x=3$, cutting it into loaves of length $3$ and $4$ for a cost of $7$.
*   Choose the loaf of length $3$ and $x=1$, cutting it into loaves of length $1$ and $2$ for a cost of $3$. Give the former to the $1$\-st child.
*   Choose the loaf of length $2$ and $x=1$, cutting it into two loaves of length $1$ for a cost of $2$. Give them to the $3$\-rd and $5$\-th children.
*   Choose the loaf of length $4$ and $x=2$, cutting it into two loaves of length $2$ for a cost of $4$. Give them to the $2$\-nd and $4$\-th children.

This incurs a cost of $7+3+2+4=16$, which is the minimum possible. There will be no leftover loaves.

Input #2

3 1000000000000000
1000000000 1000000000 1000000000

Output #2

1000005000000000

Note that each child $i$ must receive a loaf of length exactly $A_i$.

API Response (JSON)

{
  "problem": {
    "name": "Bread",
    "description": {
      "content": "We have a loaf of bread of length $L$, which we will cut and distribute to $N$ children.   The $i$\\-th child $(1\\leq i\\leq N)$ wants a loaf of length $A_i$. Now, Takahashi will repeat the operation be",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc252_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a loaf of bread of length $L$, which we will cut and distribute to $N$ children.  \nThe $i$\\-th child $(1\\leq i\\leq N)$ wants a loaf of length $A_i$.\nNow, Takahashi will repeat the operation be...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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