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)

use std::cmp::*;
use std::io::*;

mod convolution {
    use std::f64::consts::PI;
    use std::ops::{Add, Mul};
    #[derive(Clone, Copy, Debug)]
    struct Complex {
        x: f64,
        y: f64,
    }
    impl Add for Complex {
        type Output = Complex;
        fn add(self, other: Complex) -> Complex {
            Complex {
                x: self.x + other.x,
                y: self.y + other.y,
            }
        }
    }
    impl Mul for Complex {
        type Output = Complex;
        fn mul(self, other: Complex) -> Complex {
            Complex {
                x: self.x * other.x - self.y * other.y,
                y: self.x * other.y + self.y * other.x,
            }
        }
    }
    fn fft(f: &mut [Complex], n: usize, sign: f64) {
        if n == 1 {
            return;
        }
        let mut group1 = Vec::new();
        let mut group2 = Vec::new();
        for i in 0..n / 2 {
            group1.push(f[i * 2]);
            group2.push(f[i * 2 + 1])
        }
        fft(&mut group1, n / 2, sign);
        fft(&mut group2, n / 2, sign);
        let zeta = Complex {
            x: (2.0 * PI / n as f64).cos(),
            y: (2.0 * PI / n as f64).sin() * sign,
        };
        let mut now = Complex { x: 1.0, y: 0.0 };
        for i in 0..n {
            f[i] = group1[i % (n / 2)] + now * group2[i % (n / 2)];
            now = now * zeta;
        }
    }
    pub fn convolve(a: &[usize], b: &[usize]) -> Vec<usize> {
        let n = (a.len() + b.len() - 1).next_power_of_two();
        let mut f = vec![Complex { x: 0.0, y: 0.0 }; n];
        let mut g = vec![Complex { x: 0.0, y: 0.0 }; n];
        for i in 0..a.len() {
            f[i] = Complex {
                x: a[i] as f64,
                y: 0.0,
            };
            g[i] = Complex {
                x: b[i] as f64,
                y: 0.0,
            };
        }
        fft(&mut f, n, 1.0);
        fft(&mut g, n, 1.0);
        for i in 0..n {
            f[i] = f[i] * g[i];
        }
        fft(&mut f, n, -1.0);
        f.iter()
            .map(|e| (e.x / n as f64).round() as usize)
            .collect()
    }
}

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let mut m: usize = itr.next().unwrap().parse().unwrap();
    let o: Vec<usize> = (0..n)
        .map(|_| itr.next().unwrap().parse().unwrap())
        .collect();
    let mut a = vec![0; 100001];
    for i in 0..n {
        a[o[i]] += 1;
    }
    let b = a.clone();
    let c = convolution::convolve(&a, &b);

	// shukei
    let mut ans = 0;
    for i in (0..200001).rev() {
        if m == 0 {
            break;
        }
        ans += min(m, c[i]) * i;
        m -= min(m, c[i]);
    }
    println!("{}", ans);
}