Problem:
Score : 500 points

Problem Statement

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

Output

Print the maximum possible happiness after M handshakes.

Sample Input 1

5 3
10 14 19 34 33

Sample 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.

Sample Input 2

9 14
1 3 5 110 24 21 34 5 3

Sample Output 2

1837

Sample Input 3

9 73
67597 52981 5828 66249 75177 64141 40773 79105 16076

Sample Output 3

8128170

Solution in JavaScript (node.js v5.12) (judge verdict: Runtime Error)

function Main(input) {
  // 1行目がinput[0], 2行目がinput[1], …に入る
  input = input.split("\n");
  
  //入力データ取得
  var tmp0 = input[0].split(" ");
  var N = tmp0[0] - 0;
  var M = tmp0[1] - 0;
  
  var power = input[1].split(" ").map(str => parseInt(str, 10));

  var tokuten = Array(N*(N+1)/2);
  var taikaku = Array(N*(N+1)/2);
  var idx = 0;
  for(var i=0; i<N; i++){
    for(var j=0; j<=i; j++){
      tokuten[idx] = power[i] + power[j];
      if(i == j){
        taikaku[idx] = true;
      }else{
        taikaku[idx] = false;
      }
      idx++;
    }
  }
  var i=0;
  var sum = 0;
  while(i<M){
    var idx = tokuten.indexOf(Math.max.apply(null,tokuten));
    if(taikaku[idx] || i+1 == M){
      sum += tokuten[idx];
      i++
    }else{
      sum += 2*tokuten[idx];
      i+=2;
    }
    tokuten.splice(idx,1);
    taikaku.splice(idx,1);
  }
  console.log(sum);
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));