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

typedef long long ll;

const int Maxn = 100005;

int n;
ll m;
int a[Maxn];
ll S[Maxn];

ll Get(int x)
{
    ll res = 0;
    for (int i = 0; i < n; i++)
        res += a + n - upper_bound(a, a + n, x - a[i]);
    return res;
}

ll getSum(int x)
{
    ll res = 0;
    for (int i = 0; i < n; i++) {
        int ind = upper_bound(a, a + n, x - a[i]) - a;
        res += S[ind] + ll(n - ind) * a[i];
    }
    return res;
}

int main()
{
    scanf("%d %lld", &n, &m);
    for (int i = 0; i < n; i++)
        scanf("%d", &a[i]);
    sort(a, a + n);
    for (int i = n - 1; i >= 0; i--)
        S[i] = S[i + 1] + a[i];
    int l = 0, r = 2 * Maxn;
    while (l <= r) {
        int mid = l + r >> 1;
        if (Get(mid) < m) r = mid - 1;
        else l = mid + 1;
    }
    int wh = r + 1;
    ll g = Get(wh);
    ll res = getSum(wh) + (m - g) * wh;
    cout << res << endl;
    return 0;
}

### Prompt

Your challenge is to write 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 = 100005;

int n;
ll m;
int a[Maxn];
ll S[Maxn];

ll Get(int x)
{
    ll res = 0;
    for (int i = 0; i < n; i++)
        res += a + n - upper_bound(a, a + n, x - a[i]);
    return res;
}

ll getSum(int x)
{
    ll res = 0;
    for (int i = 0; i < n; i++) {
        int ind = upper_bound(a, a + n, x - a[i]) - a;
        res += S[ind] + ll(n - ind) * a[i];
    }
    return res;
}

int main()
{
    scanf("%d %lld", &n, &m);
    for (int i = 0; i < n; i++)
        scanf("%d", &a[i]);
    sort(a, a + n);
    for (int i = n - 1; i >= 0; i--)
        S[i] = S[i + 1] + a[i];
    int l = 0, r = 2 * Maxn;
    while (l <= r) {
        int mid = l + r >> 1;
        if (Get(mid) < m) r = mid - 1;
        else l = mid + 1;
    }
    int wh = r + 1;
    ll g = Get(wh);
    ll res = getSum(wh) + (m - g) * wh;
    cout << res << endl;
    return 0;
}

```