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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*; import java.io.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		Runtime rt = Runtime.getRuntime();
		long mae = System.currentTimeMillis();
		solve();flush();
		long ato = System.currentTimeMillis();
		myerr("time : " + (ato - mae) + "ms");
		myerr("memory : " + ((rt.totalMemory() - rt.freeMemory()) / 1024) + "KB");
	}
	//Don't have to see. end------------------------------------------
	static void solve(){//Here is the main function
		ArrayList<Long> one = nextLongArray();
		int N = Integer.parseInt(String.valueOf(one.get(0)));
		long M = one.get(1);
		ArrayList<Integer> list = nextIntArray();
		ArrayList<Integer> sumList2 = new ArrayList<Integer>(N);
		ArrayList<Long> sumList = new ArrayList<Long>(N);
		ArrayList<Long> maeList = new ArrayList<Long>(N);
		Collections.sort(sumList2);
		sumList2.add(0);
		for(int i = 1; i < N; i++){
			int add = sumList2.get(sumList2.size() - 1) + list.get(i - 1);
			sumList2.add(add);
		}
		Collections.sort(sumList2, Comparator.reverseOrder());
		myerr(sumList2);
		Collections.sort(list,Comparator.reverseOrder());
		myerr(list);
		long output = 0;
		long mae = 0;
		for(int i = 0; i < N; i++){
			int maxSubM = (N - i - 1) * 2 + 1;
			if(M >= maxSubM){
				output += (long) ((long)((N - i) * 2 * list.get(i)) + (long)(2 * sumList2.get(i)));
				M -= maxSubM;
			}else{
				if(M >= 1){
					output += list.get(i) * 2;
					M--;
				}
				if(M == 0){
					break;
				}
				for(int j = i + 1; j < N; j++){
					if(M >= 2){
						output += (list.get(i) + list.get(j)) * 2;
						M -= 2;
					}else if(M == 1){
						output += list.get(i) + list.get(j);
						M--;
					}
					if(M == 0){
						break;
					}
				}
			}
			/*
			myerr("mae : " + mae);
			myerr("output : " + output);
			myerr("diff : " + (output - mae));
			*/
			mae = output;
			if(M == 0){
				break;
			}
		}
		myout(output);
	}
	//Method addition frame start
 


	//Method addition frame end
}