#include<bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#define debug(x) cout << #x << ": " << x << endl
#else
#define debug(x)
#endif
typedef long long ll;
const int INF=0x3f3f3f3f;

int main()
{
	int n;
	ll m;
	cin>>n>>m;
	vector<int> a(n);
	vector<ll> suf(n+1);
	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]=suf[i+1]+a[i];
	int L=2,R=2e5,tar=-1;
	while(L<=R)
	{
		int mid=L+R>>1;
		ll cnt=0;
		for(int i=0;i<n;i++)
		{
			int pos=lower_bound(a.begin(),a.end(),mid-a[i])-a.begin();
			cnt+=n-pos;
		}
		if(cnt>=m)
		{
			L=mid+1;
			tar=mid;
		}
		else R=mid-1;
	}
	ll cnt=0,ans=0;
	for(int i=0;i<n;i++)
	{
		int pos=upper_bound(a.begin(),a.end(),tar-a[i])-a.begin();
		cnt+=n-pos;
		ans+=1ll*(n-pos)*a[i]+suf[pos];
	}
	ans+=1ll*tar*(m-cnt);
	cout<<ans<<'\n';
	return 0;
}

### Prompt

Your task is to create 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;
#ifndef ONLINE_JUDGE
#define debug(x) cout << #x << ": " << x << endl
#else
#define debug(x)
#endif
typedef long long ll;
const int INF=0x3f3f3f3f;

int main()
{
	int n;
	ll m;
	cin>>n>>m;
	vector<int> a(n);
	vector<ll> suf(n+1);
	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]=suf[i+1]+a[i];
	int L=2,R=2e5,tar=-1;
	while(L<=R)
	{
		int mid=L+R>>1;
		ll cnt=0;
		for(int i=0;i<n;i++)
		{
			int pos=lower_bound(a.begin(),a.end(),mid-a[i])-a.begin();
			cnt+=n-pos;
		}
		if(cnt>=m)
		{
			L=mid+1;
			tar=mid;
		}
		else R=mid-1;
	}
	ll cnt=0,ans=0;
	for(int i=0;i<n;i++)
	{
		int pos=upper_bound(a.begin(),a.end(),tar-a[i])-a.begin();
		cnt+=n-pos;
		ans+=1ll*(n-pos)*a[i]+suf[pos];
	}
	ans+=1ll*tar*(m-cnt);
	cout<<ans<<'\n';
	return 0;
}

```