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)

#%%
def count(a, k, n):
    l = []
    i, j, count = 0, n-1, 0
    while True:
        tmp = a[i] + a[j]
        if tmp >= k: 
            if j > 0:
                j -= 1
        elif tmp < k:
            l.append(n-j-1)
            if j < n - 1:
                j += 1
                count += n - j 
            else:
                count += n - j - 1
            i += 1
        if i >= n:
            break
        tmp = a[i] + a[j]
        if j == 0 and tmp >= k:
            l.append(n-j)
            count += n - j
            i += 1
        if i >= n:
            break
    return [count, l]

n, m = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
l, r = 10**6, 1


while l - r > 1:
    mid = (l+r)//2
    if count(a, mid, n)[0] < m:
        l = mid
    elif count(a, mid, n)[0] > m:
        r = mid
    else :
        l = mid
        r = mid
    print(l, r)

ans = 0
if l == r:
    tmp = count(a, l, n)
    for i in range(n):
        ans += a[i] * tmp[1][i] * 2
else:
    p = count(a, l, n)
    q = count(a, r, n)
    check = -1
    for i in range(n):
        if p[1][i] != q[1][i]:
            check = i
            break
    ans += (a[i] + a[n - p[1][check] - 1]) * (m - p[0])
    tmp = count(a, l, n)
    for i in range(n):
        ans += a[i] * tmp[1][i] * 2
print(ans)