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: Accepted)

import sys
import numpy as np

stdin = sys.stdin

ri = lambda: int(rs())
rl = lambda: list(map(int, stdin.readline().split())) # applies to numbers only
rs = lambda: stdin.readline().rstrip()  # ignore trailing spaces

N, M = rl()
A = np.array(rl())
A.sort()

def shake_cnt(x):
    Y = np.searchsorted(A,x-A)
    return N*N - Y.sum()

right = 10 ** 6
left = 0 #握手するのがM人以上
while right > left + 1:
    mid = (left+right) // 2
    if shake_cnt(mid) >= M:
        left = mid
    else:
        right = mid

X = np.searchsorted(A, right-A) #握手しない人数
Acum = np.zeros(N+1, np.int64)
Acum[1:] = A.cumsum()

shake = N*N - X.sum()
happy = (Acum[-1] - Acum[X]).sum() + (A * (N-X)).sum()
happy += (M-shake) * left
print(happy)