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 PYTHON3):

Solution:
'''
INPUT SHORTCUTS
N, K = map(int,input().split())
N ,A,B = map(int,input().split())
string = str(input())
arr = list(map(int,input().split()))
N = int(input())
'''


def main():
	t = int(input())
	while t:
		N, K = map(int,input().split())
		arr = list(map(int,input().split()))
		prefix = [0 for _ in range((2*K)+2)]
		cnt = [0 for _ in range((2*K)+1)]
		for i in range(len(arr)//2):
			temp = arr[i]+arr[-(i+1)]
			temp_min = min(arr[i],arr[-(i+1)])
			temp_max = max(arr[i],arr[-(i+1)])
			prefix[temp_min+1]+=1
			prefix[temp_max+K+1]+=-1
			cnt[temp]+=1
		for i in range(1,len(prefix)):
			prefix[i]+=prefix[i-1]
		min_ans = len(arr)
		for i in range(2,(2*K)+1):
			ans = (prefix[i]-cnt[i]) + (((N//2)-prefix[i])*2)
			if ans<min_ans:
				min_ans = ans
			# print(ans,prefix[i],cnt[i])
		print(min_ans)
		t-=1
main()