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: Wrong Answer)

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

internal static class CR
{
    public static string Get() { return Console.ReadLine(); }
    public static IEnumerable<string> GetTexts() { return Console.ReadLine().Split(' '); }
    public static long GetInteger() { return long.Parse(Console.ReadLine()); }
    public static IEnumerable<long> GetIntegers() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)); }
}

namespace AtCoderBeginnerContest
{
    internal class Program
    {
        public static long N { get; private set; }
        public static long M { get; private set; }
        public static List<long> A { get; private set; }

        private static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.WriteLine(r); }

        private static object GetResult()
        {
            var i1 = CR.GetIntegers().ToList();
            N = i1[0];
            M = i1[1];
            A = CR.GetIntegers().OrderByDescending(x => x).ToList();

            var patterns = GetPatterns().ToList();

            return patterns
                .Select(x => A[(int)x.RightHand] + A[(int)x.LeftHand])
                .Take((int)M)
                .Sum();
        }

        private static IEnumerable<ShakePattern> GetPatterns()
        {
            for (long i = 0; i < N; i++)
            {
                yield return new ShakePattern(i, i);

                for (long j = i + 1; j < N; j++)
                {
                    yield return new ShakePattern(i, j);
                    yield return new ShakePattern(j, i);
                }
            }
        }

        class ShakePattern
        {
            public long RightHand { get; set; }
            public long LeftHand { get; set; }

            public ShakePattern(long r, long l)
            {
                RightHand = r;
                LeftHand = l;
            }
        }
    }
}