I. Tenzing and Necklacetime limit per test2 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputbright, 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.InputEach 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.OutputFor each test case, output the minimum total time in minutes required.ExampleInput
45 21 1 1 1 15 21 2 3 4 56 34 2 5 1 3 310 32 5 6 5 2 1 7 9 7 2Output
3
7
5
15
NoteIn 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.
45 21 1 1 1 15 21 2 3 4 56 34 2 5 1 3 310 32 5 6 5 2 1 7 9 7 2
3 7 5 15 
['divide and conquer', 'dp', 'greedy', '*3500']