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

static class Program
{
    static int Search1(int N, long[] A, long n)
    {
        if (A[N - 1] >= n) { return N; }
        if (A[0] < n) { return 0; }
        int a = 0;
        int b = N - 1;
        while (b - a >= 2)
        {
            int m = (a + b) / 2;
            if (A[m] < n) { b = m; } else { a = m; }
        }
        return b;
    }

    static long Search2(int N, long[] A, long n)
    {
        return A.Sum(a => Search1(N, A, n - a));
    }

    static long Search3(int N, long M, long[] A)
    {
        if (Search2(N, A, 0) < M) { return 0; }
        long a = 0;
        long b = A[0] * 2 + 1;
        while (b - a >= 2)
        {
            long m = (a + b) / 2;
            if (Search2(N, A, m) < M) { b = m; } else { a = m; }
        }
        return a;
    }

    static long Solve(int N, long M, long[] A)
    {
        long n = Search3(N, M, A);
        var B = new long[N + 1];
        for (int i = 0; i < N; ++i) { B[i + 1] = A[i] + B[i]; }
        long cnt = 0;
        long sum = 0;
        long min = long.MaxValue;
        for (int i = 0; i < N; ++i)
        {
            int j = Search1(N, A, n - A[i]);
            cnt += j;
            sum += A[i] * j + B[j];
            if (j > 0) { min = Math.Min(A[i] + A[j - 1], min); }
        }
        return sum - min * (cnt - M);
    }

    static void Main(string[] args)
    {
        var V = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
        var A = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
        Array.Sort(A, (a, b) => (b.CompareTo(a)));
        Console.WriteLine(Solve((int)V[0], V[1], A));
    }
}