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
from itertools import accumulate

n, m, *a = map(int, sys.stdin.read().split())
a.sort()

ma = a[-1]
cnt = [0] * (ma + 1)
cur = ma
for i in range(n-1, -1, -1):
    if a[i] == cur:
        cnt[cur] += 1
    else:
        while True:
            cur -= 1
            cnt[cur] = cnt[cur+1]
            if cur == a[i]:
                cnt[cur] += 1
                break
for i in range(cur-1, -1, -1):
    cnt[i] = cnt[i+1]


def possible(border):
    pair_cnt = 0
    for i in range(n):
        aj = border - a[i]
        if aj < 0:
            aj = 0
        elif aj > ma:
            continue
        pair_cnt += cnt[aj]
    return pair_cnt >= m

def main():
    s = [0] + list(accumulate(a[::-1]))
    
    lo = 1; hi = a[-1] * 2 + 1
    while lo + 1 < hi:
        border = (lo + hi) // 2
        if possible(border):
            lo = border
        else:
            hi = border
    res = lo
    ans = 0
    minimum = float('inf')
    pair_cnt = 0
    for i in range(n):
        aj = res - a[i]
        if aj < 0:
            aj = 0
        elif aj > ma:
            continue
        c = cnt[aj]
        ans += s[c] + a[i] * c
        pair_cnt += c
        minimum = min(minimum, a[i] + a[-c])

    ans -= minimum * (pair_cnt - m)
    return ans

if __name__ == '__main__':
    ans = main()
    print(ans)