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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.util.Random;
import java.io.InputStreamReader;
import java.util.function.IntPredicate;
import java.util.Objects;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AnandOza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EHandshake solver = new EHandshake();
        solver.solve(1, in, out);
        out.close();
    }

    static class EHandshake {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long m = in.nextLong();
            int[] a = in.readIntArray(n);
            Util.safeSort(a);
            long[] prefix = new long[n + 1];
            for (int i = 0; i < n; i++) {
                prefix[i + 1] = prefix[i] + a[i];
            }

            int lambda = BinarySearch.binarySearch(l -> {
                Pair<Long, Long> result = f(a, prefix, l);

                return result.second <= m;
            });

            Pair<Long, Long> result = f(a, prefix, lambda);
            long answer = result.first + m * (long) lambda;

            out.println(answer);
        }

        private Pair<Long, Long> f(int[] a, long[] prefix, int l) {
            long answer = 0;
            long used = 0;
            for (int i = 0; i < a.length; i++) {
                int finalI = i;
                int firstGoodEnoughIndex = BinarySearch.binarySearch(index -> {
                    if (index < 0)
                        return false;
                    if (index >= a.length)
                        return true;

                    return a[finalI] + a[index] - l > 0;
                });
                long u = a.length - firstGoodEnoughIndex;
                used += u;
                answer += prefix[a.length] - prefix[firstGoodEnoughIndex];
                answer += a[i] * u - l * u;
            }

            return Pair.of(answer, used);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int[] readIntArray(int n) {
            int[] x = new int[n];
            for (int i = 0; i < n; i++) {
                x[i] = nextInt();
            }
            return x;
        }

    }

    static class Pair<F, S> {
        public final F first;
        public final S second;

        public Pair(F first, S second) {
            this.first = first;
            this.second = second;
        }

        public static <F, S> Pair<F, S> of(F first, S second) {
            return new Pair<>(first, second);
        }

        public boolean equals(Object o) {
            if (this == o)
                return true;
            if (o == null || getClass() != o.getClass())
                return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return Objects.equals(first, pair.first) && Objects.equals(second, pair.second);
        }

        public int hashCode() {
            return Objects.hash(first, second);
        }

        public String toString() {
            return "(" + first + ", " + second + ')';
        }

    }

    static class Util {
        public static void safeSort(int[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffle(int[] x) {
            Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void swap(int[] x, int i, int j) {
            int t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

    }

    static class BinarySearch {
        public static int binarySearch(IntPredicate bigEnough) {
            int tooSmall = 0, tooBig;
            if (bigEnough.test(tooSmall)) {
                return tooSmall;
            }

            for (tooBig = 1; !bigEnough.test(tooBig); tooBig *= 2)
                ;

            if (!bigEnough.test(tooBig - 1)) {
                return tooBig;
            }

            while (tooBig - tooSmall > 1) {
                int center = tooSmall + (tooBig - tooSmall) / 2;
                if (!bigEnough.test(center)) {
                    tooSmall = center;
                } else {
                    tooBig = center;
                }
            }

            return tooBig;
        }

    }
}