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.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;
 
public class Main {

	public static final MyScanner in = new MyScanner();

	public static void main(String[] args) {

        int N = in.nextInt();
        long M = in.nextLong();
        int[] A = new int[N];
        for(int i=0; i<N; i++) {
        	A[i] = in.nextInt();
        }
        Arrays.sort(A);

        int dblIdx = A.length -1;
        long score = 0;
        int cnt = 0;
        all: for(int i = A.length -1; i >=0; i--) {
        	for( int j = i-1; j >= 0; j--) {
        		while(dblIdx >=0 && A[dblIdx]*2 > A[i] + A[j]) {
        			score += A[dblIdx]*2;
        			dblIdx--;
        			if(++cnt == M) break all; 
        		}
        		score += A[i] + A[j];
    			if(++cnt == M) break all; 
        		score += A[i] + A[j];
    			if(++cnt == M) break all; 
        	}
        }

		while(dblIdx >=0 && cnt != M) {
			score += A[dblIdx]*2;
			dblIdx--;
			++cnt; 
		}

        System.out.println(score);

	}

	public static class MyScanner{
		Scanner sc = new Scanner(System.in);
		String nextLine() {return sc.nextLine();}
		String next() {return sc.next();}
		int nextInt() {return Integer.valueOf(sc.next());}
		long nextLong() { return Long.valueOf(sc.next());}
	}
}