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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

module Main where

import Data.List (nub)

getNums :: IO [Integer]
getNums = map (read :: String -> Integer) . words <$> getLine

sort :: (Ord a) => [a] -> [a]
sort = mergeAll . map (:[]) 
  where
    mergeAll [] = []
    mergeAll [t] = t
    mergeAll xs  = mergeAll (mergePairs xs)

    mergePairs (x:y:xs) = merge x y:mergePairs xs
    mergePairs xs = xs

merge :: Ord a => [a] -> [a] -> [a]
merge [] ys         = ys
merge xs []         = xs
merge (x:xs) (y:ys) | x < y     = x:merge xs (y:ys)
                    | otherwise = y:merge (x:xs) ys

main :: IO ()
main = do
    [n, m] <- map (read :: String -> Int) . words <$> getLine
    as <- getNums
    let guests = reverse . sort $ zip as [1,2..]
    let pairs = nub [(a, b) | a <- guests, b <- guests]
    let pairs' = map (\((v, i), (v', i')) -> (v, v')) pairs
    let shakeValues = reverse . sort $ map (\(a, b) -> a + b) pairs'

    let result = foldr (+) 0 (take m shakeValues)

    putStrLn $ show result