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.util.*;

class Main{

    public static void main(String args[]) throws Exception{
        Main main = new Main();
    }

    public Main(){
        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        long M = scanner.nextLong();

        int[] A = new int[N];

        for(int i=0;i<N;i++){
            A[i] = scanner.nextInt();
        }

        Arrays.sort(A);

        int L = -1, R = A[N-1]+A[N-1];
        while(R-L > 1){
            int mid = L+(R-L)/2;

            int num=0;
            for(int i=0;i<N;i++){
                int t = Arrays.binarySearch(A, mid-A[i]);
                num += N - ((t>=0) ?  t : ~t);
            }

            if(num < M)
                R = mid;
            else
                L = mid;
        }


        long[] S = new long[N+1];
        for(int i=0;i<N;i++) S[i+1] = S[i] + A[i];

        int num;
        long count=0, result = 0;
        for(int i=0;i<N;i++){
            int t = Arrays.binarySearch(A, L-A[i]);
            num = ((t>=0) ?  t : ~t);
            count += N-num;
            result += A[i]*(N-num) + S[N] - S[num];
        }

        result += L * (M - count);

        System.out.println(result);
    }
}