Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

5 3
10 14 19 34 33

Sample Output 1

202

Let us say that Takahashi performs the following handshakes:

In the first handshake, Takahashi shakes the left hand of Guest 4 and the right hand of Guest 4.

In the second handshake, Takahashi shakes the left hand of Guest 4 and the right hand of Guest 5.

In the third handshake, Takahashi shakes the left hand of Guest 5 and the right hand of Guest 4.

Then, we will have the happiness of (34+34)+(34+33)+(33+34)=202.

We cannot achieve the happiness of 203 or greater, so the answer is 202.

Sample Input 2

9 14
1 3 5 110 24 21 34 5 3

Sample Output 2

1837

Sample Input 3

9 73
67597 52981 5828 66249 75177 64141 40773 79105 16076

Sample Output 3

8128170

Solution in Rust (1.15.1) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::{fastout, input};

const INF: u64 = 1_001_001_001;

fn count_geq(a: &[u64], s: u64) -> u64 {
    let n = a.len();
    let mut res = 0u64;
    let mut t = n;
    for i in 0..n {
        while t > 0 && a[i] + a[t - 1] >= s {
            t -= 1;
        }
        res += (n - t) as u64;
    }
    res
}

fn sum_geq(a: &[u64], s: u64) -> u64 {
    let n = a.len();
    let mut asum = vec![0; n + 1];
    asum[..n].clone_from_slice(a);
    asum[n] = 0;
    for i in (0..n).rev() {
        asum[i] += asum[i + 1];
    }

    let mut res = 0u64;
    let mut t = n;
    for i in 0..n {
        while t > 0 && a[i] + a[t - 1] >= s {
            t -= 1;
        }
        res += a[i] * (n - t) as u64 + asum[t];
    }
    res
}

#[fastout]
fn main() {
    input! {
        n: usize,
        m: u64,
        mut a: [u64; n],
    }
    a.sort();

    let mut lo = 0u64;
    let mut hi = INF;
    while hi - lo > 1 {
        let mid = (hi + lo) / 2;
        if count_geq(&a, mid) >= m {
            lo = mid;
        } else {
            hi = mid;
        }
    }
    let s_least = lo;
    let s_least_cnt = m - count_geq(&a, s_least + 1);

    println!("{}", s_least * s_least_cnt + sum_geq(&a, s_least + 1));
}

*/

fn main() {
    let exe = "./binXXXXXX";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";