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 C (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
#include <math.h>

int comp(const void *a, const void *b)
{
	return *(int *)b - *(int *)a;
}

struct score {
	int score;
	int pos;
};

int comp_score(const void *a, const void *b)
{
	int as = ((struct score *)a)->score;
	int bs = ((struct score *)b)->score;
	return bs - as;
}

int main(int argc, char **argv)
{
	uint64_t N, M;
	scanf("%ld %ld", &N, &M);
	static int A[100001];
	for (int i = 0; i < N; i++)
		scanf("%d", &A[i]);
#if 0
	// sort >
	qsort(A, N, sizeof(int), comp);
	for (int i = 0; i < N; i++)
		fprintf(stderr, " %d", A[i]);
	fprintf(stderr, "\n");
#endif
#if 0
	// create matrix N*N
	struct score *matrix = calloc(sizeof(struct score), (N*N));
	for (int y = 0; y < N; y++) {
		for (int x = 0; x < N; x++) {
			matrix[y*N + x].score = A[y] + A[x];
			matrix[y*N + x].pos = y*N + x;
		}
	}
	// sort it
	qsort(matrix, N*N, sizeof(struct score), comp_score);
	for (int i = 0; i < N*N; i++)
		fprintf(stderr, "%d @ %d\n", matrix[i].score, matrix[i].pos);
	uint64_t score = 0;
	for (int i = 0; i < M; i++)
		score += matrix[i].score;
	printf("%ld\n", score);
#endif
	int *matrix = calloc(sizeof(int), (N*N));
	for (int y = 0; y < N; y++) {
		for (int x = 0; x < N; x++)
			matrix[y*N + x] = A[y] + A[x];
	}
	// sort it
	qsort(matrix, N*N, sizeof(int), comp);
	uint64_t score = 0;
	for (int i = 0; i < M; i++)
		score += matrix[i];
	printf("%ld\n", score);
	return 0;
}