#include <bits/stdc++.h>
using namespace std;
using int64 = long long;

int64 n, m;
vector<int64> a;
vector<int64> idx;
int64 sum;

bool f(int mid){
	sum = 0;
	for(int i = 0; i < n; i++){
		idx[i] = lower_bound(a.begin(), a.end(), mid - a[i]) - a.begin();
		sum += n - idx[i];
	}
	return sum >= m;
}

int main(){
	cin >> n >> m;
	a.resize(n);
	idx.resize(n);
	for(int i = 0; i < n; i++){
		cin >> a[i];
	}
	sort(a.begin(), a.end());
	int64 ans = 0;
	int64 ok = 2, ng = 1e6;
	while(ng - ok > 1){
		int64 mid = (ng + ok) / 2;
		if(f(mid)) ok = mid;
		else ng = mid;
	}
	f(ok);
	for(int i = 0; i < n; i++){
		ans += (n - idx[i]) * a[i] * 2;
	}
	ans -= (sum - m) * ok;
	cout << ans << endl;
}
### Prompt

Generate a cpp solution to the following problem:

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;
using int64 = long long;

int64 n, m;
vector<int64> a;
vector<int64> idx;
int64 sum;

bool f(int mid){
	sum = 0;
	for(int i = 0; i < n; i++){
		idx[i] = lower_bound(a.begin(), a.end(), mid - a[i]) - a.begin();
		sum += n - idx[i];
	}
	return sum >= m;
}

int main(){
	cin >> n >> m;
	a.resize(n);
	idx.resize(n);
	for(int i = 0; i < n; i++){
		cin >> a[i];
	}
	sort(a.begin(), a.end());
	int64 ans = 0;
	int64 ok = 2, ng = 1e6;
	while(ng - ok > 1){
		int64 mid = (ng + ok) / 2;
		if(f(mid)) ok = mid;
		else ng = mid;
	}
	f(ok);
	for(int i = 0; i < n; i++){
		ans += (n - idx[i]) * a[i] * 2;
	}
	ans -= (sum - m) * ok;
	cout << ans << endl;
}
```