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.IO;
using System.Linq;

namespace Handshake_2
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.SetIn(new StreamReader(Console.OpenStandardInput(8192)));
            var inputArray = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
            var _N = inputArray[0];
            var _M = inputArray[1];

            inputArray = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
            var powers = inputArray.OrderBy(x => -x).ToList();
            var accumulationPower = new List<long>();
            accumulationPower.Add(powers[0]);
            for (var i = 1; i < _N; i++)
            {
                accumulationPower.Add(accumulationPower[i - 1] + powers[i]);
            }
            var thresholdPower = powers[(int)(_N / 2)] * 2;
            var lastThresholdPower = thresholdPower;
            long maxThresholdPower = powers.First() * 2;
            long minThresholdPower = powers.Last() * 2;
            var lastCount = 0;
            long ansPower = 0;
            do
            {
                var ansCount = 0;
                for (var i = 0; i < _N; i++)
                {
                    var index = powers.FindLastIndex(x => x + powers[i] >= thresholdPower);
                    if (index > -1)
                    {
                        ansCount += (index + 1);
                    }
                }
                if(ansCount < _M)
                {
                    if(maxThresholdPower - minThresholdPower == 1)
                    {
                        ansPower = maxThresholdPower;
                        break;
                    }
                    else
                    {
                        maxThresholdPower = thresholdPower;
                        thresholdPower = (maxThresholdPower + minThresholdPower) / 2;
                    }
                }
                else if(ansCount > _M)
                {
                    if(maxThresholdPower - minThresholdPower == 1)
                    {
                        ansPower = minThresholdPower;
                        break;
                    }
                    else
                    {
                        minThresholdPower = thresholdPower;
                        thresholdPower = (maxThresholdPower + minThresholdPower) / 2;
                    }
                }
                else
                {
                    ansPower = thresholdPower;
                    break;
                }
                lastCount = ansCount;
            } while (true);

            long score = 0;
            var count = 0;
            for (var i = 0; i < _N; i++)
            {
                for(var j = 0; j < _N; j++)
                {
                    if(count < _M && powers[i] + powers[j] >= ansPower)
                    {
                        score += powers[i] + powers[j];
                        count++;
                    }
                    else
                    {
                        break;
                    }
                }
            }
            Console.WriteLine(score);
        }
    }
}