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: Time Limit Exceeded)

n, m = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
a.sort()
b = [0]
for i in reversed(a):
    b.append(b[-1] + i)


def search(i):
    if a[-1] < i:
        return 0
    mi = 0
    ma = n - 1
    while mi != ma:
        m = (mi + ma) // 2
        if a[m] >= i:
            ma = m
        else:
            mi = m + 1
    return n-mi

def countmax(i):
    ans = 0
    for j in a:
        ans += search(i - j)
    return ans

mi = 0
ma = a[-1] * 2
while mi != ma:
    md = (mi + ma) // 2 + 1
    #print(md, countmax(md))
    if countmax(md) > m:
        mi = md
    else:
        ma = md - 1

ans = 0
for j in a:
    i = search(mi + 1 - j)
    ans+=b[i]+i*j
ans += (m-countmax(mi+1))*mi
print(ans)