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 C (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>

int main(void){
  char str[1000000];
  long int N,M,A[100000];
  long int i,j,k,l,tmp,n,sum,s[100000];
  int flag=0;
  
  fgets(str,sizeof(str),stdin);
  N=atol(strtok(str," "));
  M=atol(strtok(NULL," "));
  fgets(str,sizeof(str),stdin);
  A[0]=atol(strtok(str," "));
  for(i=1;i<N;i++){
    A[i]=atol(strtok(NULL," "));
  }
  
  for(i=0;i<N;i++){
    s[i]=i;
    k=i;
    tmp=A[i];
    for(j=i+1;j<N;j++){
      if(A[j]>tmp){
        k=j;
        tmp=A[j];
      }
    }
    A[k]=A[i];
    A[i]=tmp;
  }
  
  i=0;
  n=0;
  sum=0;
  k=0;
  while(n<M){
    if(s[k]==k+1){
      k++;
    }
    tmp=A[0]+A[s[0]];
    l=0;
    for(i=0;i<k;i++){
      if(A[j]+A[s[j]]>tmp){
        tmp=A[j]+A[s[j]];
        l=i;
      }
    }
    sum+=A[l]+A[s[l]];
    n++;
    if(n==M){
      break;
    }
    if(s[l]!=l){
      sum+=A[l]+A[s[l]];
      n++;
    }
    s[l]++;
  }
  printf("%ld\n",sum);
  return 0;
}