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)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

trait Integer {
    fn close(x: Self, y: Self) -> bool;
    fn middle(x: Self, y: Self) -> Self;
}
impl Integer for usize {
    fn close(x: Self, y: Self) -> bool { x + 1 >= y }
    fn middle(x: Self, y: Self) -> Self { (x + y) / 2 }
}
impl Integer for i64 {
    fn close(x: Self, y: Self) -> bool { x + 1 >= y }
    fn middle(x: Self, y: Self) -> Self { (x + y) / 2 }
}
impl Integer for f64 {
    fn close(x: Self, y: Self) -> bool { x + 0.00000001 >= y }
    fn middle(x: Self, y: Self) -> Self { (x + y) / 2.0 }
}

// the most left element in [l, r] such that prop holds
fn binsearch<X: Integer + Copy>(l: X, r: X, prop: &Fn(X) -> bool) -> X {
    if X::close(l, r) {
        r
    } else {
        let mid = X::middle(l, r);
        if prop(mid) {
            binsearch(l, mid, prop)
        } else {
            binsearch(mid, r, prop)
        }
    }
}

// the number of elements == x
fn binsearch_count<T: Ord>(x: T, xs: &Vec<T>) -> usize {
    let n = xs.len();
    let i = binsearch(0, n, &|i| xs[i] >= x);
    let j = binsearch(0, n, &|i| xs[i] > x);
    j - i
}

// the number of elements >= x
fn binsearch_count_geq<T: Ord>(x: T, xs: &Vec<T>) -> usize {
    let n = xs.len();
    if xs[0] >= x { return n }
    n - binsearch(0, n, &|i| xs[i] >= x)
}

// the number of elements > x
fn binsearch_count_gt<T: Ord>(x: T, xs: &Vec<T>) -> usize {
    let n = xs.len();
    if xs[0] > x { return n }
    n - binsearch(0, n, &|i| xs[i] > x)
}

// the number of elements <= x
fn binsearch_count_leq<T: Ord>(x: T, xs: &Vec<T>) -> usize {
    xs.len() - binsearch_count_gt(x, &xs)
}

// the number of elements < x
fn binsearch_count_lt<T: Ord>(x: T, xs: &Vec<T>) -> usize {
    xs.len() - binsearch_count_geq(x, &xs)
}

/// z 以上になる握手の個数とその和
fn handshakes(xs: &Vec<i64>, acc: &Vec<i64>, z: i64) -> (usize, i64) {
    let n = xs.len();
    let mut count = 0;
    let mut sum = 0;
    for &x in xs.iter() {
        if z < 1 + x {
            count += n;
            sum += n as i64 * x + acc[n];
        } else if x + xs[n - 1] < z {
            continue
        } else if x + xs[0] >= z {
            count += n;
            sum += n as i64 * x + acc[n];
        } else {
            let m = binsearch_count_geq(z - x, &xs);
            count += m;
            sum += m as i64 * x + acc[n] - acc[n - m];
        }
    }
    (count, sum)
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let m: usize = sc.cin();
    let mut xs: Vec<i64> = sc.vec(n);
    xs.sort();

    let mut acc = vec![0; n + 1];
    for i in 0..n { acc[i + 1] = acc[i] + xs[i]; }

    if m == 1 { put!(xs[n-1] * 2); return }
    if m == 2 { put!(xs[n-1] * 2 + xs[n-1] + xs[n-2]); return }
    if m == 3 { put!(xs[n-1] * 2 + (xs[n-1] + xs[n-2]) * 2); return }

    let mut left = 2;  // left 以上は M 個以上ある
    let mut right = xs[n-1] * 2 + xs[0] * 2 + 100;  // right 以上は M もない
    for _ in 0..100 {
        let mid = (left + right) / 2;
        let (count, _) = handshakes(&xs, &acc, mid);
        if count >= m {
            left = mid;
        } else {
            right = mid;
        }
    }
    // for k in 1..40 { trace!(k, handshakes(&xs, &acc, k)); }
    // trace!(&xs);
    // trace!(&acc);
    // trace!(left, right);
    {
        let (count, sum) = handshakes(&xs, &acc, right);
        let ans = sum + (m - count) as i64 * (right - 1) as i64;
        put!(ans);
    }

}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}