#include<bits/stdc++.h>
using namespace std;
#define LL long long
#define maxn 100005
LL m,s[maxn*2];
int a[maxn],b[maxn*2],n;
bool check(int x){
	LL sum=0;
	for(int i=0;i<n;i++){
		if(a[i]<=x)sum+=b[x-a[i]];
		else sum+=n;
	}
	return sum>=m;
}
int main(){
	scanf("%d%lld",&n,&m);
	for(int i=0;i<n;i++){
		scanf("%d",a+i);
		b[a[i]]++,s[a[i]]+=a[i];
	}
	for(int i=99999;~i;i--)b[i]+=b[i+1],s[i]+=s[i+1];
	int l=0,r=2e5,mid;
	LL ans=0;
	while(l<=r){
		mid=(l+r)>>1;
		if(check(mid))l=mid+1;
		else r=mid-1;
	}
	for(int i=0;i<n;i++){
		if(a[i]>l)m-=n,ans+=1ll*a[i]*n+s[0];
		else m-=b[l-a[i]],ans+=1ll*a[i]*b[l-a[i]]+s[l-a[i]];
	}
	ans+=m*(l-1);
	printf("%lld\n",ans);
	return 0;
}
### 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;
#define LL long long
#define maxn 100005
LL m,s[maxn*2];
int a[maxn],b[maxn*2],n;
bool check(int x){
	LL sum=0;
	for(int i=0;i<n;i++){
		if(a[i]<=x)sum+=b[x-a[i]];
		else sum+=n;
	}
	return sum>=m;
}
int main(){
	scanf("%d%lld",&n,&m);
	for(int i=0;i<n;i++){
		scanf("%d",a+i);
		b[a[i]]++,s[a[i]]+=a[i];
	}
	for(int i=99999;~i;i--)b[i]+=b[i+1],s[i]+=s[i+1];
	int l=0,r=2e5,mid;
	LL ans=0;
	while(l<=r){
		mid=(l+r)>>1;
		if(check(mid))l=mid+1;
		else r=mid-1;
	}
	for(int i=0;i<n;i++){
		if(a[i]>l)m-=n,ans+=1ll*a[i]*n+s[0];
		else m-=b[l-a[i]],ans+=1ll*a[i]*b[l-a[i]]+s[l-a[i]];
	}
	ans+=m*(l-1);
	printf("%lld\n",ans);
	return 0;
}
```