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: Accepted)

import java.util.Scanner;

/**
 * Handshake
 */
public class Main {

    public static void main(String[] args) throws Exception {
        try (Scanner sc = new Scanner(System.in)) {
            int MAX = 100000;

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

            long[] C = new long[MAX + 2];
            for (int a : A) {
                C[a]++;
            }
            for (int i = MAX - 1; i >= 0; i--) {
                C[i] += C[i + 1];
            }

            long[] CS = new long[MAX + 2];
            for (int a : A) {
                CS[a] += a;
            }
            for (int i = MAX - 1; i >= 0; i--) {
                CS[i] += CS[i + 1];
            }

            int min = 0;
            int max = MAX * 2 + 1;

            while (Math.abs(min - max) > 1) {
                int mid = (min + max) / 2;

                long K = 0;
                for (int a : A) {
                    if (mid - a > MAX) {
                        continue;
                    }

                    K += C[Math.max(mid - a, 0)];
                }

                if (K < M) {
                    max = mid;
                } else {
                    min = mid;
                }
            }

            long H = 0;
            long K = 0;
            for (int a : A) {
                if (max - a > MAX) {
                    continue;
                }

                H += a * C[Math.max(max - a, 0)] + CS[Math.max(max - a, 0)];
                K += C[Math.max(max - a, 0)];
            }

            H += min * (M - K);

            System.out.println(H);
        }
    }

}