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 Python (3.4.3) (judge verdict: Wrong Answer)

n, m = map(int, input().split())
table = list(map(int, input().split()))

cnt = 0
table.sort(reverse=True)
goukei = 0


def plus(x, y):
    global goukei
    global cnt

    goukei += x + y
    cnt += 1
    if cnt == m:
        return True
    else:
        return False


if m == 0:
    print(0)
    quit()
for x in range(0, n):
    if plus(table[x], table[x]):
        print(goukei)
        quit()

    if m > cnt + (n - x) * (n - x - 1) + 2:
        goukei += sum([table[x] + table[y] * 2 for y in range(x + 1, n)])
        cnt += (n - x) * (n - x - 1) + 2
        if cnt >= m:
            print(goukei)
            quit()
    else:
        for y in range(x + 1, n):
            if plus(table[x], table[y]):
                print(goukei)
                quit()
            if plus(table[x], table[y]):
                print(goukei)
                quit()

print(goukei)