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

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);


    ll n,m;
    cin>>n>>m;
    ll a[n];
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    sort(a,a+n);
    ll low = -1, up = 1e15;
    while(up-low>1){
        ll mid = (up+low)/2;
        ll cnt = 0;
        for(int i=0;i<n;i++){
            cnt += a+n - lower_bound(a,a+n,mid-a[i]);
            //cerr << mid << " " << i << " " << cnt << endl;
        }
        if(cnt >= m) low = mid;
        else up = mid;
    }
    cerr << low << endl;
    ll ans = 0;
    ll cnt = 0;
    for(int i=0;i<n;i++){
        ll ret = (a+n - upper_bound(a,a+n,low-a[i]));
        ans += a[i] * ret *2;
        cnt += ret;
    }
    cerr << cnt << endl;
    ans += low * (m-cnt);
    cout << ans << 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;
typedef long long ll;

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);


    ll n,m;
    cin>>n>>m;
    ll a[n];
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    sort(a,a+n);
    ll low = -1, up = 1e15;
    while(up-low>1){
        ll mid = (up+low)/2;
        ll cnt = 0;
        for(int i=0;i<n;i++){
            cnt += a+n - lower_bound(a,a+n,mid-a[i]);
            //cerr << mid << " " << i << " " << cnt << endl;
        }
        if(cnt >= m) low = mid;
        else up = mid;
    }
    cerr << low << endl;
    ll ans = 0;
    ll cnt = 0;
    for(int i=0;i<n;i++){
        ll ret = (a+n - upper_bound(a,a+n,low-a[i]));
        ans += a[i] * ret *2;
        cnt += ret;
    }
    cerr << cnt << endl;
    ans += low * (m-cnt);
    cout << ans << endl;
    
}
```