Tenzing and Necklace

2000ms

1048576K

Description:

bright, sunny and innocent......

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.

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.

Sample Input:

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

Sample Output:

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 $$$a_1+a_2+a_4=7$$$.

Informação

Provedor Codeforces

Código CF1842I