Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in PYTHON):

Solution:
import sys
input = sys.stdin.readline
from collections import Counter

############ ---- Input Functions ---- ############
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

def print_list_int(l):
    print(" ".join(map(str, map(int, l))))


if __name__ == "__main__":
    t = inp()
    for test in range(t):
        n,k=inlt()
        arr = inlt()
        first, second = arr[:n//2], arr[-1:n//2-1:-1]
        # print(first, second)
        z = list(zip(first,second))
        targetCounts = Counter([x+y for x,y in z])
        bothOver = Counter([min(x,y)-1 for x,y in z])
        bothUnder = Counter([max(x,y)+1 for x,y in z])
        # print(targetCounts)
        # print(bothUnder)
        # print(bothOver)
        prefixUnder = Counter()
        prefix = 0
        for i in range(k+2):
            prefix += bothUnder[i]
            prefixUnder[i] = prefix
        # print(prefixUnder)
        suffixOver = Counter()
        suffix = 0
        for i in range(k+1,-1,-1):
            suffix += bothOver[i]
            suffixOver[i] = suffix
        min_replacements = n
        for target in range(2, 2*k+1):
            if target<=k:
                min_replacements = min(min_replacements, n//2 - targetCounts[target] + suffixOver[target-1])
            else:
                min_replacements = min(min_replacements, n//2 - targetCounts[target] + prefixUnder[target-k])
        print(int(min_replacements))