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;

#ifdef LOCAL 
#include "/home/gokul/Codes/lib/prettyprint.hpp"
#else
#define debug(...) 2
#endif

int main() {

  ios::sync_with_stdio(false);
  cout.tie(nullptr);
  cin.tie(nullptr);

  long long n, m;
  cin >> n >> m;

  vector<long long> a(n), suf(n + 5, 0);
  for (int i = 0; i < n; ++i) 
    cin >> a[i];

  sort(a.begin(), a.end());
  for (int i = n-1; i >= 0; --i)
    suf[i] += a[i] + suf[i+1];

  auto count = [&](int mid) {
    long long ret = 0;
    for (int i = 0, j = n-1; i < n; ++i) {
      while (j >= 0 && a[i] + a[j] >= mid) --j;
      ret += (n-j-1);  
    }
    return ret;
  };

  long long l = 0, r = 1e6;
  while (l < r) {
    int mid = (l + r) / 2;
    if (count(mid) >= m)  l = mid + 1;
    else r = mid;
  }
  
  --l;
  debug(l);
  debug(count(l));
  long long ans = 0, cnt = 0;;
  for (int i = 0; i < n; ++i) {
    int req = l - a[i];
    int j = lower_bound(a.begin(), a.end(), req) - a.begin();
    ans += suf[j];
    ans += (n-j) * a[i];
    cnt += (n-j);
  } 

  debug(suf);
  debug(cnt);
  ans -= l * (count(l) - m);
  cout << ans << '\n';
}