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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules ! read_value {($ next : expr , ($ ($ t : tt ) ,* ) ) => {($ (read_value ! ($ next , $ t ) ) ,* ) } ; ($ next : expr , [$ t : tt ; $ len : expr ] ) => {(0 ..$ len ) . map (| _ | read_value ! ($ next , $ t ) ) . collect ::< Vec < _ >> () } ; ($ next : expr , chars ) => {read_value ! ($ next , String ) . chars () . collect ::< Vec < char >> () } ; ($ next : expr , usize1 ) => {read_value ! ($ next , usize ) - 1 } ; ($ next : expr , $ t : ty ) => {$ next () . parse ::<$ t > () . expect ("Parse error" ) } ; }
#[allow(unused_macros)]
macro_rules ! input_inner {($ next : expr ) => {} ; ($ next : expr , ) => {} ; ($ next : expr , $ var : ident : $ t : tt $ ($ r : tt ) * ) => {let $ var = read_value ! ($ next , $ t ) ; input_inner ! {$ next $ ($ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! input {(source = $ s : expr , $ ($ r : tt ) * ) => {let mut iter = $ s . split_whitespace () ; let mut next = || {iter . next () . unwrap () } ; input_inner ! {next , $ ($ r ) * } } ; ($ ($ r : tt ) * ) => {let stdin = std :: io :: stdin () ; let mut bytes = std :: io :: Read :: bytes (std :: io :: BufReader :: new (stdin . lock () ) ) ; let mut next = move || -> String {bytes . by_ref () . map (| r | r . unwrap () as char ) . skip_while (| c | c . is_whitespace () ) . take_while (| c |! c . is_whitespace () ) . collect () } ; input_inner ! {next , $ ($ r ) * } } ; }

#[allow(dead_code)]
pub trait BinarySearch<T> {
    /// the first element which does not compare less than val
    fn lower_bound(&self, x: &T) -> usize;
    /// the first element which compares grater than val
    fn upper_bound(&self, x: &T) -> usize;
}
#[allow(dead_code)]
impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut ng = -1;
        let mut ok = self.len() as i32;
        while ok - ng > 1 {
            let mid = (ng + ok) / 2;
            if self[mid as usize] >= *x {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        ok as usize
    }
    fn upper_bound(&self, x: &T) -> usize {
        let mut ng = -1;
        let mut ok = self.len() as i32;
        while ok - ng > 1 {
            let mid = (ng + ok) / 2;
            if self[mid as usize] > *x {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        ok as usize
    }
}
use std::fmt::Debug;
use std::ops::{Add, Div, Sub};
#[allow(dead_code)]
/// pred: [l, r) -> bool, non-decreasing
/// return the smallest in [l, r) s.t pred(x) == true
/// if binary_search(l, r, pred) == r, pred is always false
fn binary_search<T>(l: T, r: T, pred: impl Fn(T) -> bool) -> T
where
    T: Copy + Add<Output = T> + Sub<Output = T> + Div<Output = T> + From<u8> + PartialOrd + Debug,
{
    let mut ng = l - T::from(1_u8);
    let mut ok = r;  // sentinel

    // loop invariant: pred(ng) = false, pred(ok) = true
    // pred(ng) and pred(ok) are never called
    while ok - ng > T::from(1_u8) {
        let mid = (ng + ok) / T::from(2_u8);  // ng < mid < ok
        if pred(mid) {
            ok = mid;
        } else {
            ng = mid;
        }
    }
    ok
}

/// pred: [l, r) -> bool, non-increasing
/// return the smallest in [l, r) s.t pred(x) == true
/// if binary_search2(l, r, pred) == r, pred is always false
fn binary_search2<T>(l: T, r: T, pred: impl Fn(T) -> bool) -> T
where
    T: Copy + Add<Output = T> + Sub<Output = T> + Div<Output = T> + From<u8> + PartialOrd + Debug,
{
    let ng = binary_search(l - T::from(1_u8), r - T::from(1_u8), |x| !pred(x));
    if ng == l {
        r
    } else {
        ng - T::from(1_u8)
    }
}

fn main() {
    input! {
        n: usize,
        m: i64,
        a_: [i64; n],
    }
    let mut a = a_.clone();
    a.sort();

    // pred(x) == true iff the number of pairs whose sum is >= x is less than m
    let pred = |x| {
        let mut cnt = 0;
        for i in 0..n {
            cnt += n - a.lower_bound(&(x - a[i]));
        }
        (cnt as i64) >= m
    };
    let x = binary_search2(0, 1e11 as i64, pred);
    dbg!(x);

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

    let mut ret = 0;
    let mut cnt = 0;
    for i in (0..n).rev() {
        let j = a.lower_bound(&(x - a[i]));
        ret += cum[n] - cum[j] + a[i] * (n - j) as i64;
        cnt += n - j;
    }
    ret -= x * (cnt as i64 - m);
    println!("{}", ret)
}
// 1 3 3 5 5 21 24 34 110