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 num::Complex;
use proconio::input;
use std::f64::consts::PI;

fn fft(a: &mut Vec<Complex<f64>>, n: usize, sign: f64) {
    if n == 1 {
        return;
    }
    let mut a0 = vec![Complex::new(0., 0.); n / 2];
    let mut a1 = vec![Complex::new(0., 0.); n / 2];
    for i in 0..n / 2 {
        a0[i] = a[i * 2];
        a1[i] = a[i * 2 + 1];
    }
    fft(&mut a0, n / 2, sign);
    fft(&mut a1, n / 2, sign);
    let mut w = Complex::new(1., 0.);
    let w0 = (Complex::i() * 2. * PI * sign / n as f64).exp();
    for i in 0..n / 2 {
        let t = w * a1[i];
        a[i] = a0[i] + t;
        a[n / 2 + i] = a0[i] - t;
        w *= w0;
    }
}

fn main() {
    input! {
      n: usize,
      mut m: usize,
      a: [usize; n],
    }
    let a_max = a.iter().max().unwrap().clone();
    let mut l = 1;
    while l <= a_max {
        l *= 2;
    }
    l *= 2;
    let mut x = vec![Complex::new(0f64, 0.); l];
    let mut y = vec![Complex::new(0f64, 0.); l];
    for i in 0..n {
        x[a[i]].re += 1.;
        y[a[i]].re += 1.;
    }
    // println!("{:?}", x);
    fft(&mut x, l, 1.);
    fft(&mut y, l, 1.);
    for i in 0..l {
        x[i] *= y[i];
    }
    fft(&mut x, l, -1.);
    for i in 0..l {
        x[i] /= l as f64;
    }
    // println!("{:?}", x);

    let mut s = 0;
    for i in 0..l {
        let b = l - 1 - i;
        let k = x[b].re.round() as usize;
        if k != 0 {
            let k = if k > m { m } else { k };
            // println!("{} {}", b, k);
            s += k * b;
            m -= k;
            if m == 0 {
                break;
            }
        }
    }
    println!("{}", s);
}
*/

fn main() {
    let exe = "/tmp/bin0B0146BA";
    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>";