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.*;

public class Main{
    static Scanner sc = new Scanner(System.in);

    static int n = sc.nextInt();

    public static void main(String[] args) {

        long m = sc.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = sc.nextLong();
        Arrays.sort(a);

        long left = 0;
        long right = a[n-1]*2+1;
        while (left<right){
            long mid = (left+right)/2;
            long c = numberOfHandshake(mid, a);
            if (c<=m){
                right = mid;
            }else {
                left = mid+1;
            }
        }
        long c = numberOfHandshake(left, a);
        long h = totalHappiness(left, a);
        if (c<m){
            h += (left-1)*(m-c);
        }
        System.out.println(h);
    }


    public static long numberOfHandshake(long x, long[] a){
        int n = a.length;
        long ret = 0;
        for (int i=0; i<n; i++){
            ret += n - lowerbound(x-a[i], a);
        }
        return ret;
    }

    public static long totalHappiness(long x, long[] a){
        int n = a.length;
        long[] sum = new long[n+1];
        for (int i=0; i<n; i++){
            sum[i+1] = sum[i] + a[i];
        }
        long ret = 0;
        for (int i=0; i<n; i++){
            int idx = lowerbound(x-a[i], a);
            ret += sum[n]-sum[idx]+(n-idx)*a[i];
        }
        return ret;
    }


    public static int lowerbound(long value, long[] arr){
        int left = 0;
        int right = arr.length;
        if (arr[n-1]<value){
            return n;
        }
        if (arr[0]>=value){
            return 0;
        }
        while (left<right){
            int mid = (left+right)/2;
            if (arr[mid]<value){
                left = mid+1;
            }else {
                right = mid;
            }
        }
        return left;
    }
}