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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import java.io.*;
public class Main {
    public static void main(String[] args) throws Exception {
        InputStreamReader r = new InputStreamReader(System.in);
        int X = 1000;
        int N = nextInt(r);
        long M = nextInt(r);
        int[] A = new int[N];
        int[][] B = new int[N*N/X+1][X];
        int c = 0;
        int d = 0;
        for (int i = 0; i < N; i++) {
            A[i] = nextInt(r);
            for (int j = i; j >= 0; j--) {
                B[d][c] = A[i]+A[j];
                sortB(X, B, c, d);
                c++;
                if (c == X) {
                    d++;
                    c = 0;
                }
                if (i != j) {
                    B[d][c] = A[i]+A[j];
                    sortB(X, B, c, d);
                    c++;
                    if (c == X) {
                        d++;
                        c = 0;
                    }
                }
            }
        }

        int ans = 0;
        int cnt = 0;
        for (int i = 0; i < N*N/X+1; i++) {
            if (cnt >= M) break;
            for (int j = 0; j < X; j++) {
                if (cnt >= M) break;
                ans += B[i][j];
                cnt++;
            }
        }
        System.out.println(ans);
    }

    public static int nextInt(InputStreamReader r) throws Exception {
        String str = "";
        while (true) {
            int c = r.read();
            if (c == 32 || c == 10 || c == -1) {
                break;
            }
            str += (char)c;
        }
        return Integer.parseInt(str);
    }

    public static void sortB(int X, int[][] B, int c, int d) {
        for (int k = c; k >= 0; k--) {
            if (d >= 1 && k == 0 && B[d][k] > B[d-1][X-1]) {
                int tmp = B[d-1][X-1];
                B[d-1][X-1] = B[d][k];
                B[d][k] = tmp;
                sortB(X, B, X-1, d-1);
            } else if (k >= 1 && B[d][k] > B[d][k-1]) {
                int tmp = B[d][k-1];
                B[d][k-1] = B[d][k];
                B[d][k] = tmp;
            } else {
                break;
            }
        }
    }
}