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 Go (1.6) (judge verdict: Runtime Error)

package main

import (
	"os"
	"bufio"
	"strconv"
	"fmt"
	"sort"
)

func main() {
	var result int
	var scores []int
	n := scanInt()
	m := scanInt()
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = scanInt()
	}

	// 降順にソート
	sort.Sort(sort.Reverse(sort.IntSlice(a)))

	// 全組み合わせ分の獲得点数を取得
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			scores = append(scores, a[i] + a[j])
		}
	}

	// 降順にソート
	sort.Sort(sort.Reverse(sort.IntSlice(scores)))

	// 加算
	for i := 0; i < m; i++ {
		result += scores[i]
	}

	fmt.Printf("%d", result)
}

var scanStdin = func() *bufio.Scanner {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
	return scanner
}()

func scanString() string {
	scanStdin.Scan()
	return scanStdin.Text()
}

func scanInt() int {
	result, err := strconv.Atoi(scanString())
	if err != nil {
		panic(err)
	}
	return result
}