#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define all(x) x.begin(), x.end()
typedef long long ll;

int main() {
    ll N, M; cin >> N >> M;
    vector<ll> A(N);
    rep(i, N) cin >> A[i];
    rep(i, N) A[i] = -A[i];
    sort(all(A));
    ll val = -1;
    ll lo = 0, hi = 1e12;
    while(lo <= hi) {
        ll mid = (lo + hi) >> 1;
        ll cnt = 0;
        rep(i, N) {
            cnt += upper_bound(all(A), -mid - A[i]) - A.begin();
        }
        if(cnt >= M) {
            val = -mid;
            lo = mid + 1;
        } else hi = mid - 1;
    }
    ll sum = 0, cnt = 0;
    rep(i, N) {
        ll c = upper_bound(all(A), val - A[i]) - A.begin();
        sum += -A[i] * c;
        cnt += c;
    }
    sum *= 2;
    sum += (M - cnt) * -val;
    cout << sum << endl;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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.

Examples

Input

5 3
10 14 19 34 33


Output

202


Input

9 14
1 3 5 110 24 21 34 5 3


Output

1837


Input

9 73
67597 52981 5828 66249 75177 64141 40773 79105 16076


Output

8128170

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define all(x) x.begin(), x.end()
typedef long long ll;

int main() {
    ll N, M; cin >> N >> M;
    vector<ll> A(N);
    rep(i, N) cin >> A[i];
    rep(i, N) A[i] = -A[i];
    sort(all(A));
    ll val = -1;
    ll lo = 0, hi = 1e12;
    while(lo <= hi) {
        ll mid = (lo + hi) >> 1;
        ll cnt = 0;
        rep(i, N) {
            cnt += upper_bound(all(A), -mid - A[i]) - A.begin();
        }
        if(cnt >= M) {
            val = -mid;
            lo = mid + 1;
        } else hi = mid - 1;
    }
    ll sum = 0, cnt = 0;
    rep(i, N) {
        ll c = upper_bound(all(A), val - A[i]) - A.begin();
        sum += -A[i] * c;
        cnt += c;
    }
    sum *= 2;
    sum += (M - cnt) * -val;
    cout << sum << endl;
}
```