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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

int main()
{
    ll n,m;
    cin>>n>>m;
    ll arr[n];
    for(int i=0;i<n;i++)
        cin>>arr[i];
    sort(arr,arr+n);
    reverse(arr,arr+n);
    ll sum=0;
    ll pre[n];
    pre[0]=arr[0];
    for(int i=1;i<n;i++)
        pre[i]=pre[i-1]+arr[i];
    for(int i=0;i<n;i++)
    {
        if(m>0)
            {sum+=(arr[i]+arr[i]);m--;}
        ll p=min(m/2,n-i-1);
        if(p==(n-i-1))
        {
            m-=(2*(n-i-1));
            ll ss=((n-i-1)*arr[i] + (pre[n-1]-pre[i]));
            sum+=(2*ss);
        }
        else
        {
            ll ss=((m/2)*arr[i] + (pre[m/2+i]-pre[i]));
            sum+=(2*ss);
            if(m&1)
                sum+=(arr[i]+arr[m/2+i]);
            break;
        }
    }
    cout<<sum;
}