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.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.ABC_149
{
    class E
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            long[] nm = ReadLongs();
            long n = nm[0];
            long m = nm[1];
            long[] array = ReadLongs();
            Array.Sort(array);
            Array.Reverse(array);

            long bottom = 0;
            long top = 300000;
            while (bottom + 1 < top)
            {
                long mid = (bottom + top) / 2;
                long cnt = 0;
                for(int i = 0; i < n; i++)
                {
                    if (mid > array[i] + array[0]) continue;
                    long bottom2 = 0;
                    long top2 = n;
                    while (bottom2 + 1 < top2)
                    {
                        long mid2 = (bottom2 + top2) / 2;
                        if (array[i] + array[mid2] >= mid) bottom2 = mid2;
                        else top2 = mid2;
                    }
                    cnt += bottom2 + 1;
                }
                if (cnt >= m) bottom = mid;
                else top = mid;
            }

            long resCnt = 0;
            long res = 0;
            long[] sums = new long[n];
            for(int i = 0; i < n; i++)
            {
                sums[i] = array[i];
                if (i > 0) sums[i] += sums[i - 1];
            }
            for(int i = 0; i < n; i++)
            {
                if (bottom > array[i] + array[0]) continue;
                long bottom2 = 0;
                long top2 = n;
                while (bottom2 + 1 < top2)
                {
                    long mid2 = (bottom2 + top2) / 2;
                    if (array[i] + array[mid2] >= bottom) bottom2 = mid2;
                    else top2 = mid2;
                }
                resCnt += bottom2 + 1;
                res += sums[bottom2] + array[i] * (bottom2 + 1);
            }
            res -= (resCnt - m) * bottom;
            WriteLine(res);
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}