E - Amusement Park

Score : $500$ points

Problem Statement

Takahashi has come to an amusement park.
The park has $N$ attractions. The fun of the $i$-th attraction is initially $a_i$.

When Takahashi rides the $i$-th attraction, the following sequence of events happens.

• Takahashi's satisfaction increases by the current fun of the $i$-th attraction.
• Then, the fun of the $i$-th attraction decreases by $1$.

Takahashi's satisfaction is initially $0$. He can ride the attractions at most $K$ times in total in any order.
What is the maximum possible value of satisfaction Takahashi can end up with?

Other than riding the attractions, nothing affects Takahashi's satisfaction.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq K \leq 2 \times 10^9$
• $1 \leq A_i \leq 2 \times 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the maximum possible value of satisfaction that Takahashi can end up with.

3 5
100 50 102

502

Takahashi should ride the first attraction twice and the third attraction three times.
He will end up with the satisfaction of $(100+99)+(102+101+100)=502$.
There is no way to get the satisfaction of $503$ or more, so the answer is $502$.

2 2021
2 3

9

Takahashi may choose to ride the attractions fewer than $K$ times in total.