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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace PGC
{
	class Program
	{
		static void Main(string[] args)
		{
			var header = Console.ReadLine().Split().Select(long.Parse).ToArray();
			var N = header[0];
			var M = header[1];
			var A = Console.ReadLine().Split().Select(long.Parse).ToArray();

			var fixA = A.OrderBy(a => a).Reverse().ToArray();

			var b = new long[N + 1];
			for (var i = 0; i < N; i++)
			{
				b[i + 1] = b[i] + fixA[i];
			}

			var aMax = 2 * 100000 + 1;
			var d = new int[aMax];

			for (var i = 0; i < N; i++)
			{
				d[fixA[i]]++;
			}
			for (var i = aMax - 1; 1 <= i; i--)
			{
				d[i - 1] += d[i];
			}

			var left = -1;
			var right = aMax;
			while (1 < right - left)
			{
				var mid = (right + left) / 2;
				var s = 0L;
				for (var i = 0; i < N; i++)
				{
					s += d[Math.Max(1, mid - fixA[i])];
				}
				if (M <= s)
				{
					left = mid;
				}
				else
				{
					right = mid;
				}
			}

			var ans = 0L;
			var ss = 0L;

			for (var i = 0; i < N; i++)
			{
				var v = Math.Max(0, right - fixA[i]);
				var t = Math.Max(0, Math.Min(d[v], M - ss));
				ans += b[t] + t * fixA[i];
				ss += t;
			}

			ans += left * (M - ss);
			System.Console.WriteLine(ans);
		}
	}
}