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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

int main()
{
    int N;
    long M;
    cin >> N >> M;
    int *A = new int[N];
    for (int i = 0; i < N; i++)
    {
        cin >> A[i];
    }
    sort(A, A + N);
    long long **SUM = new long long *[N];
    for (int i = 0; i < N; i++)
    {
        SUM[i] = new long long[N];
    }
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
        {
            SUM[i][j] = static_cast<long long>(A[i] + A[j]);
        }
    }

    int l = static_cast<int>(SUM[0][0]), r = static_cast<int>(SUM[N - 1][N - 1]);
    int shake, mid = (l + r) / 2, oldmid=0;
    while (oldmid!=mid)
    {
        oldmid = mid;
        shake = 0;
        int y = N - 1;
        for (int x = 0; x < N; x++)
        {
            if(y < 0){
                shake += N;
                continue;
            }
            while (static_cast<int>(SUM[y][x]) >= mid)
            {
                y--;
                if (y < 0)
                {
                    break;
                }
            }
            shake += N - y - 1;
        }
        if (shake < M)
        {
            r = mid;
        }
        else
        {
            if (shake > M)
            {
                l = mid;
            }
            else
            {
                break;
            }
        }
        mid = (l + r) / 2;
    }

    int remind = mid * (shake - M);
    for (int x = 0; x < N; x++)
    {
        for (int y = 0; y < N; y++)
        {
            if (static_cast<int>(SUM[y][x]) < mid)
            {
                SUM[y][x] = 0;
            }
            else
            {
                if (y != 0)
                {
                    SUM[y][x] += SUM[y - 1][x];
                }
                if (x != 0)
                {
                    SUM[y][x] += SUM[y][x - 1];
                }
                if(x!=0&&y!=0){
                    SUM[y][x] -= SUM[y-1][x-1];
                }
            }
        }
    }

    cout << SUM[N - 1][N - 1] - static_cast<long long>(remind) << "\n";

    return 0;
}