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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n, m = gets.split.map &:to_i
as = gets.split.map &:to_i

#as = []
#100000.times {
# as << (rand * 100000).ceil
#}

as.sort!{|a, b| b <=> a}

cand_i = [[0,0]]
cand = [as[0] + as[0]]

point = 0

searched = {}
searched[[0,0]] = true

m.times{
	i = cand.each_with_index.max[1]
	point += cand[i]
	
	if cand_i[i][0] < n - 1 && searched[[cand_i[i][0] + 1, cand_i[i][1]]] == nil then
		searched[[cand_i[i][0] + 1, cand_i[i][1]]] = true
		cand_i << [cand_i[i][0] + 1, cand_i[i][1]]
		cand << as[cand_i[i][0] + 1] + as[cand_i[i][1]]
	end
	if cand_i[i][1] < n - 1 && searched[[cand_i[i][0], cand_i[i][1] + 1]] == nil then
		searched[[cand_i[i][0], cand_i[i][1] + 1]] = true
		cand_i << [cand_i[i][0], cand_i[i][1] + 1]
		cand << as[cand_i[i][0]] + as[cand_i[i][1] + 1]
	end

	cand_i.delete_at(i)
	cand.delete_at(i)

}

puts point