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

const int maxn=1e5+7;
int n,a[maxn];
long long s[maxn],m,ans,cnt;

int main()
{
	scanf("%d %lld",&n,&m);
	for(int i=1;i<=n;++i) {
		scanf("%d",a+i);
	}
	sort(a+1,a+n+1);
	for(int i=1;i<=n;++i) {
		s[i]=s[i-1]+a[i];
	}
	int l=0,r=3e5;
	while(l+1<r) {
		int mid=(l+r)>>1;
		cnt=0;
		for(int i=1;i<=n;++i) {
			int c=lower_bound(a+1,a+n+1,mid-a[i])-a;
			cnt+=n-c+1;
		}
		if(cnt>=m) l=mid;
		else r=mid;
	}
	cnt=0;
	for(int i=1;i<=n;++i) {
		int c=upper_bound(a+1,a+n+1,l-a[i])-a;
		ans+=1ll*(n-c+1)*a[i]+s[n]-s[c-1];
		cnt+=n-c+1;
	}
	ans+=(m-cnt)*l;
	printf("%lld",ans);
}
### Prompt

Please formulate 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;

const int maxn=1e5+7;
int n,a[maxn];
long long s[maxn],m,ans,cnt;

int main()
{
	scanf("%d %lld",&n,&m);
	for(int i=1;i<=n;++i) {
		scanf("%d",a+i);
	}
	sort(a+1,a+n+1);
	for(int i=1;i<=n;++i) {
		s[i]=s[i-1]+a[i];
	}
	int l=0,r=3e5;
	while(l+1<r) {
		int mid=(l+r)>>1;
		cnt=0;
		for(int i=1;i<=n;++i) {
			int c=lower_bound(a+1,a+n+1,mid-a[i])-a;
			cnt+=n-c+1;
		}
		if(cnt>=m) l=mid;
		else r=mid;
	}
	cnt=0;
	for(int i=1;i<=n;++i) {
		int c=upper_bound(a+1,a+n+1,l-a[i])-a;
		ans+=1ll*(n-c+1)*a[i]+s[n]-s[c-1];
		cnt+=n-c+1;
	}
	ans+=(m-cnt)*l;
	printf("%lld",ans);
}
```