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)

#from collections import *
#from itertools import *
#from bisect import *
from heapq import *
#import copy
#N=int(input())
#X,Y=map(int,input().split())
#S=list(map(int,input().split()))
#S=[list(map(int,input().split())) for i in range(N)]

N,M=map(int,input().split())
A=sorted(list(map(int,input().split())),reverse=True)
"""
lst=[]
for i in range(N):
    for m in range(N):
        lst.append(A[i]+A[m])
lst=sorted(lst,reverse=True)
print(sum(lst[:M]))"""


ng=-1
ok=10**10+1
while ok>ng+1:
    mid=(ok+ng)//2
    K=0
    idx=0
    for i in range(N-1,-1,-1):

        X=mid-A[i]
        while idx<N and A[idx]>=X:
            idx+=1
        K+=idx


    if K>M:
        ng=mid
    else:
        ok=mid
#print(mid)
idx=0
lst=[0 for i in range(N)]
for i in range(N-1,-1,-1):
    X=mid-A[i]
    while idx<N and A[idx]>=X:
        idx+=1
    lst[i]=idx*2
value=0
for a,i in zip(A,lst):
    value+=a*i

value-=mid*(sum(lst)//2-M)

print(value)