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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import bisect
N,M=map(int,input().split())
A=list(map(int,input().split()))
A=sorted(A)
B=[0]*N
B[-1]=A[-1]
for i in range(1,N):
    B[-1-i]=B[-i]+A[-i-1]

L=[0]*N
Max=A[-1]*2+1
Min=A[0]*2
s=0

while(s!=M):
    s=0
    l=Max
    r=Min
    C=(l+r)//2
    c=0
    for i in range(N):
        w=C-A[i]
        t=N-bisect.bisect(A,w)
        s+=t

    if(s<M):
        if(Max==C):
            break
        Max=C
    elif(s>M):
        if(Min==C):
            break
        Min=C
#print(C,M,s)
S=0
J=0
for i in range(N):
    w=C-A[i]
    a=bisect.bisect(A,w)
    t=N-a
    if t>0:
        S+=t*A[i]+B[-t]
    if(N==a):
        a-=1
    x=A[i]+A[a]
    if x>C and abs(C-J)>abs(C-x):
        J=x

print(S-J*(s-M))