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)

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

namespace Contest
{
    partial class Program
    {
        static void Main(string[] args)
        {
            ABC149E();
        }

        static void ABC149A()
        {
            var st = ReadStrN();
            Console.WriteLine("{0}{1}", st[1], st[0]);
        }
        static void ABC149B()
        {
            var abk = ReadLongN();
            var A1 = Math.Max(0, abk[0] - abk[2]);
            var B1 = Math.Max(0, Math.Min(abk[1], abk[0] + abk[1] - abk[2]));
            Console.WriteLine("{0} {1}", A1, B1);
        }
        static void ABC149C()
        {
            var X = ReadInt();
            for(int i = X; i <= X * 2; ++i)
            {
                if (Util.IsPrime(i))
                {
                    Console.WriteLine(i);
                    return;
                }
            }
        }
        static void ABC149D()
        {
            var nk = ReadIntN();
            var rsp = ReadIntN();
            var str = ReadStr();
            var N = nk[0];
            var K = nk[1];
            var R = rsp[0];
            var S = rsp[1];
            var P = rsp[2];

            var dp = new int[N + 1, 3];
            for(int i = 0; i < N; ++i)
            {
                var c = str[i];
                dp[i + 1, 0] = (i + 1 >= K ? Math.Max(dp[i + 1 - K, 1], dp[i + 1 - K, 2]) : 0) + (c == 's' ? R : 0);
                dp[i + 1, 1] = (i + 1 >= K ? Math.Max(dp[i + 1 - K, 0], dp[i + 1 - K, 2]) : 0) + (c == 'p' ? S : 0);
                dp[i + 1, 2] = (i + 1 >= K ? Math.Max(dp[i + 1 - K, 0], dp[i + 1 - K, 1]) : 0) + (c == 'r' ? P : 0);
            }
            var result = Enumerable.Range(0, K).Select(i => Enumerable.Range(0, 3).Select(j => dp[N - i, j]).Max()).Sum();
            Console.WriteLine(result);
        }
        static void ABC149E()
        {
            var nm = ReadIntN();
            var A = ReadIntN();
            var N = nm[0];
            var M = nm[1];

            A = A.OrderBy(x => x).ToArray();
            Func<int, int> func = X => {
                int count = 0;
                int right = N;
                for (int left = 0; left < N; ++left)
                {
                    while (right > 0 && A[left] + A[right - 1] >= X)
                    {
                        right--;
                    }
                    count += (N - right);
                }
                return count;
            };

            int min = 1;
            int max = 200000;
            while (min + 1 < max)
            {
                var mid = (min + max) / 2;
                var count = func(mid);
                if (count < M)
                {
                    max = mid;
                }
                else
                {
                    min = mid;
                }
            }

            var ASum = new long[N + 1];
            for (int i = 0; i < N; ++i)
            {
                ASum[i + 1] = ASum[i] + A[i];
            }
            {
                var X = min;
                long sum = 0;
                int count = 0;
                int right = N;
                for (int left = 0; left < N; ++left)
                {
                    while (right > 0 && A[left] + A[right - 1] >= X)
                    {
                        right--;
                    }
                    count += (N - right);
                    sum += A[left] * (N - right) + ASum[N] - ASum[right];
                }
                sum -= (count - M) * X;
                Console.WriteLine(sum);
            }
        }

        class Util
        {
            public static readonly long P = 1000000007;

            public static long Sum(long[] array)
            {
                return Sum(array, array.Length);
            }
            public static long Sum(long[] array, int n)
            {
                long total = 0;
                for(int i = 0; i < n; ++i)
                {
                    total += array[i];
                }
                return total;
            }
            public static long Count(long[] array, long x)
            {
                return Count(array, x, array.Length);
            }
            public static long Count(long[] array, long x, int n)
            {
                long total = 0;
                for (int i = 0; i < n; ++i)
                {
                    total += (array[i] == x ? 1 : 0);
                }
                return total;
            }

            public static long GCD(long a, long b)
            {
                while (b > 0)
                {
                    var c = a % b;
                    a = b;
                    b = c;
                }
                return a;
            }
            public static bool IsPrime(long x)
            {
                var fact = Factorize(x);
                return fact.Count == 1 && fact.Values.ElementAt(0) == 1;
            }
            public static Dictionary<long,int> Factorize(long x)
            {
                var dict = new Dictionary<long, int>();
                long minp = 2;
                while (x > 1)
                {
                    bool ok = false;
                    for(long p = minp; p * p <= x; ++p)
                    {
                        if (x % p == 0)
                        {
                            if (!dict.ContainsKey(p))
                            {
                                dict.Add(p, 0);
                            }
                            dict[p]++;
                            minp = p;
                            x /= p;
                            ok = true;
                            break;
                        }
                    }
                    if (!ok)
                    {
                        if (!dict.ContainsKey(x)) { dict.Add(x, 0); }
                        dict[x]++;
                        break;
                    }
                }
                return dict;
            }
            public static long Inverse(long a, long p)
            {
                long b = p, c = 1, d = 0, e = 0, f = 0;
                while (b != 0)
                {
                    e = a / b;
                    f = b; b = a - e * b; a = f;
                    f = d; d = c - e * d; c = f;
                }
                c %= p;
                return c + (c < 0 ? p : 0);
            }
            public static long[] Facts(int n, long p)
            {
                var facts = new long[n + 1];
                facts[0] = 1;
                for (int i = 1; i <= n; ++i)
                {
                    facts[i] = (i * facts[i - 1]) % p;
                }
                return facts;
            }
            public static Func<int,int,long> Combin(int n, long P)
            {
                var fact = Facts(n, P);
                var inv = fact.Select(x => Inverse(x, P)).ToArray();
                return (N, M) =>
                {
                    if (N < 0 || N < M || M < 0) { return 0; }
                    return (((fact[N] * inv[M]) % P) * inv[N - M]) % P;
                };
            }

            /// <summary>
            /// Calc Combin(n,m) where n is large and m<=mMax
            /// </summary>
            public static Func<int,int,long> CombinLarge(int mMax, long p)
            {
                var inv = Enumerable.Range(0, mMax + 1).Select(x => Util.Inverse(x, Util.P)).ToArray();
                return (n, m) =>
                {
                    long mult = 1;
                    for (int i = 1; i <= m; ++i)
                    {
                        mult = (((mult * (n + 1 - i)) % Util.P) * inv[i]) % Util.P;
                    }
                    return mult;
                };
            }

            /// <summary>
            /// Calc 2^n mod p
            /// </summary>
            public static long Power2(long n, long p)
            {
                return Power(2, n, p);
            }
            public static long Power(long a, long n, long p)
            {
                long res = 1;
                long mult = a;
                for (int i = 0; i < 40; ++i)
                {
                    if ((n & ((long)1 << i)) > 0)
                    {
                        res = (res * mult) % p;
                    }
                    mult = (mult * mult) % p;
                }
                return res;
            }
        }
        class Geometric
        {
            /// <summary>
            /// 2点間の距離
            /// </summary>
            public static double Distance(Tuple<double, double> s, Tuple<double, double> t)
            {
                var diff1 = s.Item1 - t.Item1;
                var diff2 = s.Item2 - t.Item2;
                return Math.Sqrt(diff1 * diff1 + diff2 * diff2);
            }
            /// <summary>
            /// 2点の中点
            /// </summary>
            public static Tuple<double,double> Center(Tuple<double, double> s, Tuple<double, double> t)
            {
                return new Tuple<double, double>((s.Item1 + t.Item1) / 2, (s.Item2 + t.Item2) / 2);
            }

            /// <summary>
            /// 垂直二等分線 ax+by+c=0の係数(a,b,c)を出力
            /// </summary>
            public static Tuple<double,double,double> Bisector(Tuple<double, double> s, Tuple<double, double> t)
            {
                var a = t.Item1 - s.Item1;
                var b = t.Item2 - s.Item2;
                var c = -a * (s.Item1 + t.Item1) / 2 - b * (s.Item2 + t.Item2) / 2;
                return new Tuple<double, double, double>(a, b, c);
            }

            /// <summary>
            /// 2本の直線が平行か(絶対誤差Epsilon)
            /// </summary>
            public static bool IsParallel(Tuple<double, double, double> line1, Tuple<double, double, double> line2, double epsilon)
            {
                return Math.Abs(line1.Item1 * line2.Item2 - line1.Item2 * line2.Item1) < epsilon;
            }

            /// <summary>
            /// 2本の直線の交点(平行でないことを仮定)
            /// </summary>
            public static Tuple<double,double> Intersection(Tuple<double, double, double> line1, Tuple<double, double, double> line2)
            {
                var div = line1.Item1 * line2.Item2 - line1.Item2 * line2.Item1;
                var x = (line1.Item2 * line2.Item3 - line1.Item3 * line2.Item2) / div;
                var y = (line1.Item3 * line2.Item1 - line1.Item1 * line2.Item3) / div;
                return new Tuple<double, double>(x, y);
            }
        }

        struct MOD
        {
            public static long P = 1000000007;
            public readonly long V;

            public MOD(long a) { this.V = a; }
            public static implicit operator MOD(long a) { return new MOD(a); }
            public static MOD operator +(MOD a, MOD b) { return new MOD((a.V + b.V) % P); }
            public static MOD operator -(MOD a, MOD b) { return new MOD((a.V - b.V + P) % P); }
            public static MOD operator *(MOD a, MOD b) { return new MOD((a.V * b.V) % P); }
            public static MOD operator /(MOD a, MOD b) { return new MOD((a.V * b.Inverse().V) % P); }
            public MOD Inverse() { return Util.Inverse(V, P); }
            public MOD Power(long n) { return Util.Power(V, n, P); }
        }

        static string ReadStr()
        {
            return Console.ReadLine();
        }
        static string[] ReadStrN()
        {
            return Console.ReadLine().Split(' ');
        }
        static int ReadInt()
        {
            return Convert.ToInt32(Console.ReadLine());
        }
        static int[] ReadIntN()
        {
            return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
        }
        static long ReadLong()
        {
            return Convert.ToInt64(Console.ReadLine());
        }
        static long[] ReadLongN()
        {
            return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
        }
        static Tuple<string, string>[] ReadTupleStr(int n)
        {
            List<Tuple<string, string>> list = new List<Tuple<string, string>>();
            for (int i = 0; i < n; ++i)
            {
                var ab = ReadStrN();
                list.Add(new Tuple<string, string>(ab[0], ab[1]));
            }
            return list.ToArray();
        }
        static Tuple<long, long>[] ReadTupleLong(int n)
        {
            List<Tuple<long, long>> list = new List<Tuple<long, long>>();
            for (int i = 0; i < n; ++i)
            {
                var ab = ReadLongN();
                list.Add(new Tuple<long, long>(ab[0], ab[1]));
            }
            return list.ToArray();
        }
        static Tuple<double, double>[] ReadTupleDouble(int n)
        {
            List<Tuple<double, double>> list = new List<Tuple<double, double>>();
            for (int i = 0; i < n; ++i)
            {
                var ab = ReadLongN();
                list.Add(new Tuple<double, double>(ab[0], ab[1]));
            }
            return list.ToArray();
        }
    }
}