Tenzing and Necklace
Description
Tenzing has a beautiful necklace. The necklace consists of $n$ pearls numbered from $1$ to $n$ with a string connecting pearls $i$ and $(i \text{ mod } n)+1$ for all $1 \leq i \leq n$.
One day Tenzing wants to cut the necklace into several parts by cutting some strings. But for each connected part of the necklace, there should not be more than $k$ pearls. The time needed to cut each string may not be the same. Tenzing needs to spend $a_i$ minutes cutting the string between pearls $i$ and $(i \text{ mod } n)+1$.
Tenzing wants to know the minimum time in minutes to cut the necklace such that each connected part will not have more than $k$ pearls.
Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 10^5$) — the number of test cases. The description of test cases follows.
The first line of each test case contains two integers $n$ and $k$ ($2\leq n\leq 5\cdot 10^5$, $1\leq k <n$).
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i\leq 10^9$).
It is guaranteed that the sum of $n$ of all test cases does not exceed $5 \cdot 10^5$.
For each test case, output the minimum total time in minutes required.
Input
Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 10^5$) — the number of test cases. The description of test cases follows.
The first line of each test case contains two integers $n$ and $k$ ($2\leq n\leq 5\cdot 10^5$, $1\leq k <n$).
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i\leq 10^9$).
It is guaranteed that the sum of $n$ of all test cases does not exceed $5 \cdot 10^5$.
Output
For each test case, output the minimum total time in minutes required.
4
5 2
1 1 1 1 1
5 2
1 2 3 4 5
6 3
4 2 5 1 3 3
10 3
2 5 6 5 2 1 7 9 7 2
3
7
5
15
Note
In the first test case, the necklace will be cut into $3$ parts: $[1,2][3,4][5]$, so the total time is $3$.
In the second test case, the necklace will be cut into $3$ parts: $[5,1][2][3,4]$, Tenzing will cut the strings connecting $(1,2), (2,3)$ and $(4,5)$, so the total time is $a_1+a_2+a_4=7$.