#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MAXN = 200005;
int n, a[MAXN], cnt[MAXN];
LL val[MAXN], m;
int main () {
	scanf("%d%lld", &n, &m);
	for(int i = 1; i <= n; ++i) scanf("%d", &a[i]), ++cnt[a[i]], val[a[i]] += a[i];
	sort(a + 1, a + n + 1);
	for(int i = 100000; i >= 1; --i) cnt[i] += cnt[i+1], val[i] += val[i+1];
	int l = 0, r = 200000, mid;
	LL tot;
	while(l < r) {
		mid = (l + r + 1) >> 1;
		tot = 0;
		for(int i = 1; i <= n; ++i) tot += cnt[max(1,mid-a[i])];
		if(tot >= m) l = mid;
		else r = mid - 1;
	}
	LL ans = 0; tot = 0;
	for(int i = 1; i <= n; ++i) ans += val[max(1, l+1-a[i])]+1ll*a[i]*cnt[max(1, l+1-a[i])], tot += cnt[max(1, l+1-a[i])];
	m -= tot;
	ans += m*l;
	printf("%lld\n", ans);
}
### 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;
typedef long long LL;
const int MAXN = 200005;
int n, a[MAXN], cnt[MAXN];
LL val[MAXN], m;
int main () {
	scanf("%d%lld", &n, &m);
	for(int i = 1; i <= n; ++i) scanf("%d", &a[i]), ++cnt[a[i]], val[a[i]] += a[i];
	sort(a + 1, a + n + 1);
	for(int i = 100000; i >= 1; --i) cnt[i] += cnt[i+1], val[i] += val[i+1];
	int l = 0, r = 200000, mid;
	LL tot;
	while(l < r) {
		mid = (l + r + 1) >> 1;
		tot = 0;
		for(int i = 1; i <= n; ++i) tot += cnt[max(1,mid-a[i])];
		if(tot >= m) l = mid;
		else r = mid - 1;
	}
	LL ans = 0; tot = 0;
	for(int i = 1; i <= n; ++i) ans += val[max(1, l+1-a[i])]+1ll*a[i]*cnt[max(1, l+1-a[i])], tot += cnt[max(1, l+1-a[i])];
	m -= tot;
	ans += m*l;
	printf("%lld\n", ans);
}
```