Home

Contest: Task: Related: TaskD TaskF

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

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

Sample Input 3

9 73
67597 52981 5828 66249 75177 64141 40773 79105 16076