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)

import sys
sys.setrecursionlimit(10**9)
N,M=map(int,input().split())
A=list(map(int,input().split()))
A=sorted(A)[::-1]
ans=A[0]*2
M-=1
flg=False
kiroku=[0]*N
def nibu(l,r,x,X):
  global A
  mid=(l+r)//2
  if X+A[mid] == x*2 or l+1==r:
    return mid
  elif X+A[mid] > x*2:
    return nibu(mid,r,x,X)
  else:
    return nibu(l,mid,x,X)

i=0
while M>0:
  if i+1>=N:
    flg=True
    break
  j=nibu(i,N-1,A[i+1],A[i])
  kiroku[i]=j
  if (j-i)*2>M:
    m=M//2
    for k in range(i+1,i+1+m):
      ans+=(A[i]+A[k])*2
      M-=2
    ans+=(A[i]+A[i+1+m])
    M-=1
    break
  else:
    for k in range(i+1,j+1):
      ans+=(A[i]+A[k])*2
    M-=(j-i)*2
  i+=1
  if M>0:
    ans+=A[0]*2
    M-=1
if flg:
  for i in range(N):
    for j in range(kiroku[i]+1,N):
      if i+1==j and M>1:
        ans+=A[i]*2
        M-=1
      if M>1:
        ans+=(A[i]+A[j])*2
        M-=2
      else:
        ans+=(A[i]+A[j])
        M-=1
      if M==0:
        break
print(ans)