human
Write me a Python code to find this maximum possible sum given the following:
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...
assistant
#Here is Python code to find this maximum possible sum.

import sys

def main():
    def modst(a, s):
        ret = 1
        while s:
            if s % 2:
                ret = ret * a % mod
            a = a * a % mod
            s //= 2
        return ret   
    #n, v, u = map(int, sys.stdin.readline().split())
    n, k = map(int, sys.stdin.readline().split())
    #n = int(sys.stdin.readline().strip())
    #a, b = map(int, sys.stdin.readline().split())
    #q = sorted(list(map(int, sys.stdin.readline().split())))
    q = sorted(list(map(int, sys.stdin.readline().split())), reverse=True)
    res, fl, h, i = 0, 0, n // 2 + 1, n // 2
    while fl < k:
        fl += 1
        res += q[i]
        i += h
    print(res)

    
        
    
        
    
    
            
    
    
         
    
for i in range(int(sys.stdin.readline().strip())):
    main()