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: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        new Main().solve(System.in, System.out);
    }

    public void solve(InputStream in, PrintStream out) {
        Scanner sc = new Scanner(in);
        int n = sc.nextInt();
        long m = sc.nextLong();
        long[] a = new long[n];
        long[] sum = new long[n+1];
        for(int i=0; i<n; i++) {
            a[i] = sc.nextInt();
        }
        Arrays.sort(a);
        for(int i=0; i<n; i++) {
            sum[i+1] = sum[i] + a[i];
        }

        long l = 0;
        long r = a[n-1] * 2 + 1;
        long mid;
        while(l + 1 < r) {
            mid = (l+r)/2;
            long count = 0;
            for(int i=0; i<n; i++) {
                long min = mid - a[i];
                int ind = Arrays.binarySearch(a, min);
                if(ind < 0) {
                    ind = - 1 - ind;
                }
                count += n - ind;
            }
            if(count < m) {
                r = mid;
            } else {
                l = mid;
            }
        }
        long score = 0;
        long count = 0;
        for(int i=0; i<n; i++) {
            long min = l - a[i];
            int ind = Arrays.binarySearch(a, min);
            if(ind < 0) {
                ind = - 1 - ind;
            }
            count += n - ind;
            score += a[i] * (n-ind);
            score += sum[n] - sum[ind];
        }
        score -= (count - m) * l;
        out.println(score);
    }
}