Handshake

AtCoder

IDabc149_e

Time2000ms

Memory256MB

Difficulty—

Takahashi has come to a party as a special guest. There are $N$ ordinary guests at the party. The $i$\-th ordinary guest has a _power_ of $A_i$. Takahashi has decided to perform $M$ _handshakes_ to increase the _happiness_ of the party (let the current happiness be $0$). A handshake will be performed as follows: * Takahashi chooses one (ordinary) guest $x$ for his left hand and another guest $y$ for his right hand ($x$ and $y$ can be the same). * Then, he shakes the left hand of Guest $x$ and the right hand of Guest $y$ simultaneously to increase the happiness by $A_x+A_y$. However, Takahashi should not perform the same handshake more than once. Formally, the following condition must hold: * Assume that, in the $k$\-th handshake, Takahashi shakes the left hand of Guest $x_k$ and the right hand of Guest $y_k$. Then, there is no pair $p, q$ $(1 \leq p < q \leq M)$ such that $(x_p,y_p)=(x_q,y_q)$. What is the maximum possible happiness after $M$ handshakes? ## Constraints * $1 \leq N \leq 10^5$ * $1 \leq M \leq N^2$ * $1 \leq A_i \leq 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

5 3
10 14 19 34 33

Output #1

202

Let us say that Takahashi performs the following handshakes:

*   In the first handshake, Takahashi shakes the left hand of Guest $4$ and the right hand of Guest $4$.
*   In the second handshake, Takahashi shakes the left hand of Guest $4$ and the right hand of Guest $5$.
*   In the third handshake, Takahashi shakes the left hand of Guest $5$ and the right hand of Guest $4$.

Then, we will have the happiness of $(34+34)+(34+33)+(33+34)=202$.
We cannot achieve the happiness of $203$ or greater, so the answer is $202$.

Input #2

9 14
1 3 5 110 24 21 34 5 3

Output #2

Input #3

9 73
67597 52981 5828 66249 75177 64141 40773 79105 16076

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Handshake",
    "description": {
      "content": "Takahashi has come to a party as a special guest. There are $N$ ordinary guests at the party. The $i$\\-th ordinary guest has a _power_ of $A_i$. Takahashi has decided to perform $M$ _handshakes_ to in",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc149_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has come to a party as a special guest. There are $N$ ordinary guests at the party. The $i$\\-th ordinary guest has a _power_ of $A_i$.\nTakahashi has decided to perform $M$ _handshakes_ to in...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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