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: Runtime Error)

#region いつもの
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using static Global;
using static NumGlobal;

static class Global
{
    public static T[] NewArray<T>(int len0, T value) => new T[len0].Fill(value);
    public static T[] NewArray<T>(int len0, Func<T> factory)
    {
        var arr = new T[len0];
        for (int i = 0; i < arr.Length; i++) arr[i] = factory();
        return arr;
    }
    public static T[][] NewArray<T>(int len0, int len1, T value) where T : struct
    {
        var arr = new T[len0][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, value);
        return arr;
    }
    public static T[][] NewArray<T>(int len0, int len1, Func<T> factory)
    {
        var arr = new T[len0][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, factory);
        return arr;
    }
    public static T[][][] NewArray<T>(int len0, int len1, int len2, T value) where T : struct
    {
        var arr = new T[len0][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, value);
        return arr;
    }
    public static T[][][] NewArray<T>(int len0, int len1, int len2, Func<T> factory)
    {
        var arr = new T[len0][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, factory);
        return arr;
    }
    public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, T value) where T : struct
    {
        var arr = new T[len0][][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, value);
        return arr;
    }
    public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, Func<T> factory)
    {
        var arr = new T[len0][][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, factory);
        return arr;
    }
    private class ComparerReverseImpl<T> : Comparer<T> where T : IComparable<T> { public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); }
    public static IComparer<T> ComparerReverse<T>() where T : IComparable<T> => new ComparerReverseImpl<T>();
    public static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    public static string AllJoin<T>(IEnumerable<T> source) => string.Join(" ", source);
}
static class NumGlobal
{
    public static int Pow(int x, int y)
    {
        int res = 1;
        for (; y > 0; y >>= 1)
        {
            if ((y & 1) == 1) res *= x;
            x *= x;
        }
        return res;
    }
    public static BigInteger ParseBigInteger(string s)
    {
        // MonoのBigInteger.Parseが遅いので自前実装
        var res = BigInteger.Zero;
        var splited = new string[(s.Length + 7) / 8];
        for (var i = 0; i < splited.Length - 1; i++)
        {
            splited[i] = s.Substring(8 * i, 8);
        }
        splited[splited.Length - 1] = s.Substring(8 * (splited.Length - 1));
        foreach (var sp in splited)
        {
            res *= (int)Math.Pow(10, sp.Length);
            res += int.Parse(sp);
        }
        return res;
    }
    public static int BitCount(int x) { x -= (x >> 1) & 0x55555555; x = (x & 0x33333333) + ((x >> 2) & 0x33333333); x = (x + (x >> 4)) & 0x0f0f0f0f; x += x >> 8; x += x >> 16; return x & 0x3f; }
    public static int BitCount(long x) { x -= (x >> 1) & 0x5555555555555555; x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333); x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f; x += x >> 8; x += x >> 16; x += x >> 32; return (int)(x & 0x0000007f); }
    public static int MSB(int x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; return BitCount(x) - 1; }
    public static int MSB(long x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; x |= x >> 32; return BitCount(x) - 1; }
    public static int LSB(int x) { x |= x << 1; x |= x << 2; x |= x << 4; x |= x << 8; x |= x << 16; return 32 - BitCount(x); }
    public static int LSB(long x) { x |= x << 1; x |= x << 2; x |= x << 4; x |= x << 8; x |= x << 16; x |= x << 32; return 64 - BitCount(x); }
}
static class Ext
{
    public static T[] Fill<T>(this T[] arr, T value)
    {
        for (var i = 0; i < arr.Length; i++) arr[i] = value;
        return arr;
    }
    public static T[] Sort<T>(this T[] arr)
    {
        Array.Sort(arr);
        return arr;
    }
    public static string[] Sort(this string[] arr)
    {
        Array.Sort(arr, StringComparer.OrdinalIgnoreCase);
        return arr;
    }
    public static T[] Reverse<T>(this T[] arr)
    {
        Array.Reverse(arr);
        return arr;
    }

    public static Tuple<TSource, TMax> MaxBy<TSource, TMax>
        (this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector)
        where TMax : IComparable<TMax>
    {
        TMax max;
        TSource maxByItem;

        var e = source.GetEnumerator();
        e.MoveNext();
        maxByItem = e.Current;
        max = maxBySelector(maxByItem);
        while (e.MoveNext())
        {
            var item = e.Current;
            var next = maxBySelector(item);
            if (max.CompareTo(next) < 0)
            {
                max = next;
                maxByItem = item;
            }
        }
        return Tuple.Create(maxByItem, max);
    }
    public static Tuple<TSource, TMin> MinBy<TSource, TMin>
        (this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector)
        where TMin : IComparable<TMin>
    {
        TMin min;
        TSource minByItem;

        var e = source.GetEnumerator();
        e.MoveNext();
        minByItem = e.Current;
        min = minBySelector(minByItem);
        while (e.MoveNext())
        {
            var item = e.Current;
            var next = minBySelector(item);
            if (min.CompareTo(next) > 0)
            {
                min = next;
                minByItem = item;
            }
        }
        return Tuple.Create(minByItem, min);
    }
    public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
    public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
    public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
}
#pragma warning disable CA1819
public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public int Int0 => Int - 1; public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { public SplitLine(ConsoleReader cr) { String = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String { get; } } public SplitLine Split => new SplitLine(this); public class RepeatReader { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (int i = 0; i < count; i++) arr[i] = factory(cr); return arr; } public string[] String => this.Select(cr => cr.String); public int[] Int => this.Select(cr => cr.Int); public int[] Int0 => this.Select(cr => cr.Int - 1); public long[] Long => this.Select(cr => cr.Long); public double[] Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
public class Program
{
    [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader cr;

    public Program(ConsoleReader consoleReader) { this.cr = consoleReader; }
    static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc());

    #endregion
    public object Calc()
    {
        cr = new ConsoleReader(new System.IO.StreamReader(@"Z:\source\repos\AtCoderProject\AtCoderTest\input.txt"));

        var N = cr.Int;
        M = cr.Long;
        a = cr.Split.Int.Sort();
        int min = 0;
        int r = (int)1e6;
        while (min < r)
        {
            var m = (min + r + 1) >> 1;
            if (Calc(m) >= M) min = m;
            else r = m - 1;
        }

        var sums = new Sums(a);
        long cnt = (M - Calc(min + 1)) * min;
        r = a.Length;
        for (int i = 0; i < a.Length; i++)
        {
            while (r > 0 && a[i] + a[r - 1] > min) r--;
            cnt += sums[r, a.Length] + (long)a[i] * (a.Length - r);
        }

        return cnt;
    }

    long Calc(int v)
    {
        int r = a.Length;
        var cnt = 0L;
        for (int i = 0; i < a.Length; i++)
        {
            while (r > 0 && a[i] + a[r - 1] >= v) r--;
            cnt += a.Length - r;
        }

        return cnt;
    }

    long M;
    int[] a;
}
class Sums
{
    private long[] impl;
    public int Length { get; }
    public Sums(int[] arr)
    {
        this.Length = arr.Length;
        impl = new long[arr.Length + 1];
        for (var i = 0; i < arr.Length; i++)
            impl[i + 1] = impl[i] + arr[i];
    }
    public long this[int toExclusive]
    {
        get { return impl[toExclusive]; }
    }
    public long this[int from, int toExclusive]
    {
        get { return impl[toExclusive] - impl[from]; }
    }
}