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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int m = scanner.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = scanner.nextInt();
		}
		scanner.close();
		Arrays.parallelSort(a);

		int min = a[0] + a[0]; //m=n^2
		int sup = a[n - 1] + a[n - 1] + 1; //m=0
		int mid;
		while (sup - min > 1) {
			mid = (min + sup) / 2;
			if (countHandShake(mid, n, a) >= m) {
				min = mid;
			} else {
				sup = mid;
			}
		}

		long sum = 0;
		int left = 0;
		int right = n - 1;
		while (left <= right) {
			if (a[left] + a[right] >= min) {
				for (int i = left; i < right; i++)
					sum += (a[i] + a[right]) * 2;
				sum += a[right] * 2;
				right--;
			} else {
				left++;
			}

		}
		sum -= min * (countHandShake(min, n, a) - m);

		System.out.println(sum);

	}

	static long countHandShake(int threshold, int n, int[] a) {
		long count = 0;
		int left = 0;
		int right = n - 1;
		while (left <= right) {
			if (a[left] + a[right] >= threshold) {
				count += (right - left) * 2 + 1;
				right--;
			} else {
				left++;
			}

		}
		return count;
	}

}