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: Accepted)

#include <bits/stdc++.h>
 
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<ll, ll> pii;
 
#define REP(a,b,c) for(ll (a)=(b);(a)<(c);(a)++)
#define PER(a,b,c) for(ll (a)=(b);(a)>=(c);(a)--)

int main(){
    ll N, M;
    vector<ll> A;
    ll AMAX=(ll)1E5;
    vector<ll> S(AMAX+10,0);

    cin >> N >> M;
    REP(i,0,N){
        ll a;
        cin >> a;
        A.push_back(a);
        S[A[i]]++;
    }
    sort(A.begin(), A.end());

    PER(i,AMAX,0){
        S[i]+=S[i+1];
    }

    ll l=0,r=AMAX*2+10;
    ll t=0;
    while(r-l>1){
        ll m=(l+r)/2;
        ll num = 0;
        REP(i,0,N){
            ll target=max(min(m-A[i],AMAX+1),(ll)0);
            num += S[target];
        }
        if(num >= M){
            l = m;
            t = num;
        }else{
            r = m;
        }
    }

    ll ret=0;
    REP(i,0,N){
        ll target=max(min(l-A[i],AMAX+1),(ll)0);
        ret += A[i] * S[target] * 2;
    }
    cout << ret - (t - M) * l << endl;
    
    return 0;
}