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: Accepted)

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

namespace Handshake_3
{
    class Program
    {
        static void Main(string[] args)
        {
            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();

            long top1 = powers.First() * 2 + 1;
            long bottom1 = -1;
            var powerIndex = new List<long[]>((int)_N);
            long thresholdPower = 0;
            do
            {
                powerIndex.Clear();
                long count = 0;
                var mid1 = (top1 + bottom1) / 2;
                for (var i = 0; i < _N; i++)
                {
                    long top2 = _N;
                    long bottom2 = -1;
                    do
                    {
                        var mid2 = (top2 + bottom2) / 2;
                        if (powers[i] + powers[(int)mid2] >= mid1)
                        {
                            bottom2 = mid2;
                        }
                        else
                        {
                            top2 = mid2;
                        }
                    } while (top2 - bottom2 > 1);
                    count += top2;
                    powerIndex.Add(new long[2] { powers[i], top2 });
                }

                if(count >= _M)
                {
                    bottom1 = mid1;
                    thresholdPower = mid1;
                }
                else
                {
                    top1 = mid1;
                }
            } while (top1 - bottom1 > 1);

            var accumulation = new long[_N + 1];
            accumulation[0] = 0;
            for (var i = 0; i < _N; i++)
            {
                accumulation[i + 1] = accumulation[i] + powers[i];
            }

            {
                long ans = 0;
                long count = 0;
                foreach (var item in powerIndex)
                {
                    ans += (item[0] * item[1] + accumulation[item[1]]);
                    count += item[1];
                }
                ans -= (count - _M) * thresholdPower;
                Console.WriteLine(ans);
            }
        }
    }
}