| Codeforces Round 796 (Div. 1) |
|---|
| Finished |
Marisa comes to pick mushrooms in the Enchanted Forest.
The Enchanted forest can be represented by $$$n$$$ points on the $$$X$$$-axis numbered $$$1$$$ through $$$n$$$. Before Marisa started, her friend, Patchouli, used magic to detect the initial number of mushroom on each point, represented by $$$a_1,a_2,\ldots,a_n$$$.
Marisa can start out atany point in the forest on minute $$$0$$$. Each minute, the followings happen in order:
- She moves from point $$$x$$$ to $$$y$$$ ($$$|x-y|\le 1$$$, possibly $$$y=x$$$).
- She collects all mushrooms on point $$$y$$$.
- A new mushroom appears on each point in the forest.
Note that shecannot collect mushrooms on minute $$$0$$$.
Now, Marisa wants to know the maximum number of mushrooms she can pick after $$$k$$$ minutes.
Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of the test cases follows.
The first line of each test case contains two integers $$$n$$$, $$$k$$$ ($$$1 \le n \le 2 \cdot 10 ^ 5$$$, $$$1\le k \le 10^9$$$) — the number of positions with mushrooms and the time Marisa has, respectively.
The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the initial number of mushrooms on point $$$1,2,\ldots,n$$$.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10 ^ 5$$$.
For each test case, print the maximum number of mushrooms Marisa can pick after $$$k$$$ minutes.
45 25 6 1 2 35 75 6 1 2 31 29999995 700001000000000 1000000000 1000000000 1000000000 1000000000
123710000005000349985
Test case 1:
Marisa can start at $$$x=2$$$. In the first minute, she moves to $$$x=1$$$ and collect $$$5$$$ mushrooms. The number of mushrooms will be $$$[1,7,2,3,4]$$$. In the second minute, she moves to $$$x=2$$$ and collects $$$7$$$ mushrooms. The numbers of mushrooms will be $$$[2,1,3,4,5]$$$. After $$$2$$$ minutes, Marisa collects $$$12$$$ mushrooms.
It can be shown that it is impossible to collect more than $$$12$$$ mushrooms.
Test case 2:
This is one of her possible moving path:
$$$2 \rightarrow 3 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5$$$
It can be shown that it is impossible to collect more than $$$37$$$ mushrooms.
| Name |
|---|