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.