#D3447. Sum of Medians
Sum of Medians
Sum of Medians
A median of an array of integers of length n is the number standing on the ⌈ {n/2} ⌉ (rounding up) position in the non-decreasing ordering of its elements. Positions are numbered starting with 1. For example, a median of the array [2, 6, 4, 1, 3, 5] is equal to 3. There exist some other definitions of the median, but in this problem, we will use the described one.
Given two integers n and k and non-decreasing array of nk integers. Divide all numbers into k arrays of size n, such that each number belongs to exactly one array.
You want the sum of medians of all k arrays to be the maximum possible. Find this maximum possible sum.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The next 2t lines contain descriptions of test cases.
The first line of the description of each test case contains two integers n, k (1 ≤ n, k ≤ 1000).
The second line of the description of each test case contains nk integers a_1, a_2, …, a_{nk} (0 ≤ a_i ≤ 10^9) — given array. It is guaranteed that the array is non-decreasing: a_1 ≤ a_2 ≤ … ≤ a_{nk}.
It is guaranteed that the sum of nk for all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case print a single integer — the maximum possible sum of medians of all k arrays.
Example
Input
6 2 4 0 24 34 58 62 64 69 78 2 2 27 61 81 91 4 3 2 4 16 18 21 27 36 53 82 91 92 95 3 4 3 11 12 22 33 35 38 67 69 71 94 99 2 1 11 41 3 3 1 1 1 1 1 1 1 1 1
Output
165 108 145 234 11 3
Note
The examples of possible divisions into arrays for all test cases of the first test:
Test case 1: [0, 24], [34, 58], [62, 64], [69, 78]. The medians are 0, 34, 62, 69. Their sum is 165.
Test case 2: [27, 61], [81, 91]. The medians are 27, 81. Their sum is 108.
Test case 3: [2, 91, 92, 95], [4, 36, 53, 82], [16, 18, 21, 27]. The medians are 91, 36, 18. Their sum is 145.
Test case 4: [3, 33, 35], [11, 94, 99], [12, 38, 67], [22, 69, 71]. The medians are 33, 94, 38, 69. Their sum is 234.
Test case 5: [11, 41]. The median is 11. The sum of the only median is 11.
Test case 6: [1, 1, 1], [1, 1, 1], [1, 1, 1]. The medians are 1, 1, 1. Their sum is 3.
inputFormat
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The next 2t lines contain descriptions of test cases.
The first line of the description of each test case contains two integers n, k (1 ≤ n, k ≤ 1000).
The second line of the description of each test case contains nk integers a_1, a_2, …, a_{nk} (0 ≤ a_i ≤ 10^9) — given array. It is guaranteed that the array is non-decreasing: a_1 ≤ a_2 ≤ … ≤ a_{nk}.
It is guaranteed that the sum of nk for all test cases does not exceed 2 ⋅ 10^5.
outputFormat
Output
For each test case print a single integer — the maximum possible sum of medians of all k arrays.
Example
Input
6 2 4 0 24 34 58 62 64 69 78 2 2 27 61 81 91 4 3 2 4 16 18 21 27 36 53 82 91 92 95 3 4 3 11 12 22 33 35 38 67 69 71 94 99 2 1 11 41 3 3 1 1 1 1 1 1 1 1 1
Output
165 108 145 234 11 3
Note
The examples of possible divisions into arrays for all test cases of the first test:
Test case 1: [0, 24], [34, 58], [62, 64], [69, 78]. The medians are 0, 34, 62, 69. Their sum is 165.
Test case 2: [27, 61], [81, 91]. The medians are 27, 81. Their sum is 108.
Test case 3: [2, 91, 92, 95], [4, 36, 53, 82], [16, 18, 21, 27]. The medians are 91, 36, 18. Their sum is 145.
Test case 4: [3, 33, 35], [11, 94, 99], [12, 38, 67], [22, 69, 71]. The medians are 33, 94, 38, 69. Their sum is 234.
Test case 5: [11, 41]. The median is 11. The sum of the only median is 11.
Test case 6: [1, 1, 1], [1, 1, 1], [1, 1, 1]. The medians are 1, 1, 1. Their sum is 3.
样例
6
2 4
0 24 34 58 62 64 69 78
2 2
27 61 81 91
4 3
2 4 16 18 21 27 36 53 82 91 92 95
3 4
3 11 12 22 33 35 38 67 69 71 94 99
2 1
11 41
3 3
1 1 1 1 1 1 1 1 1
165
108
145
234
11
3