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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace Handshake
{
    class Program
    {
        static void Main(string[] args)
        {
            var inputStr = ReadlLongLine();
            var inputArray = inputStr.Split(' ').Select(x => int.Parse(x)).ToArray();
            var _N = inputArray[0];
            var _M = inputArray[1];

            inputStr = ReadlLongLine();
            inputArray = inputStr.Split(' ').Select(x => int.Parse(x)).ToArray();
            var powers = inputArray.OrderBy(x => -x).ToList();
            var totalList = new List<int>();
            var count = powers.Count();
            for (var i = 0; i < _N; i++)
            {
                for (var j = i; j < _N; j++)
                {
                    var power = powers[i] + powers[j];
                    var loopCount = (i == j) ? 1 : 2;
                    var endFlg = false;
                    for(var k = 0; k < loopCount; k++)
                    {
                        if (totalList.Count < _M)
                        {
                            totalList.Add(power);
                        }
                        else
                        {
                            var min = totalList.Min();
                            if (min < power)
                            {
                                totalList.Remove(min);
                                totalList.Add(power);
                            }
                            else
                            {
                                endFlg = true;
                                break;
                            }
                        }
                    }
                    if (endFlg)
                    {
                        break;
                    }

                }
            }
            Console.WriteLine(totalList.Sum());
        }

        static public string ReadlLongLine()
        {
            var bytes = new List<byte>();
            do
            {
                var c = Console.Read();
                bytes.Add((byte)c);
            } while (!(bytes.Count >= 2 && bytes[bytes.Count - 2] == 0x0D && bytes[bytes.Count - 1] == 0x0A));

            return System.Text.Encoding.ASCII.GetString(bytes.ToArray());
        }
    }
}