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 <stdlib.h>
#include <assert.h>
#include <string.h>
#include <errno.h> 
int main(){
    int n,m;
    scanf("%d %d",&n,&m);
    int* a=(int*)malloc(sizeof(int)*n);
    int* b=(int*)malloc(sizeof(int)*n*n);
    int c=0;
    for(int i=0;i<n;i++){
        scanf("%d",&a[i]);
        for(int j=0;j<i;j++){
            b[c]=(a[i]+a[j]);
            c++;
            b[c]=(a[i]+a[j]);
            c++;
        }
        b[c]=(a[i]+a[i]);
        c++;
    }
    int total=c-1;
    int tmp;
    for (int i=0; i<total; ++i) {
    for (int j=i+1; j<total; ++j) {
      if (b[i] < b[j]) {
        tmp =  b[i];
        b[i] = b[j];
        b[j] = tmp;
      }
    }
    }
    int s=0;
    for(int i=0;i<m;i++){
        s+=b[i];
    }
    printf("%d",s);
}