Score : $500$ points

问题陈述

高桥来到了一个游乐园。
该游乐园共有 $N$ 个游乐设施。第 $i$ 个游乐设施的初始乐趣值为 $a_i$。

当高桥乘坐第 $i$ 个游乐设施时，会发生以下事件序列：

• 高桥的 满意度 将会增加当前第 $i$ 个游乐设施的乐趣值。
• 然后，第 $i$ 个游乐设施的乐趣值减少 $1$。

高桥的满意度初始为 $0$。他最多可以任意顺序乘坐游乐设施总共 $K$ 次。
高桥最终可能获得的最大满意度是多少？

除了乘坐游乐设施外，没有任何因素会影响高桥的满意度。

以上为通义千问 qwen-max 翻译，仅供参考。

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.

Sample Input 1

3 5
100 50 102

Sample Output 1

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 $502$.

Sample Input 2

2 2021
2 3

Sample Output 2

9

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

update @ 2024/3/10 09:35:14