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 at any 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 she cannot collect mushrooms on minute $0$.

Now, Marisa wants to know the maximum number of mushrooms she can pick after $k$ minutes.

Input

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 $2 \cdot 10 ^ 5$.

Output

For each test case, print the maximum number of mushrooms Marisa can pick after $k$ minutes.

见题面 Input 部分

见题面 Output 部分

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.