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:
def solve(arr,s,k):
	hs = s // 2 
	bal = max(arr)
	unchanged1 = [0]*(bal+k+2)
	unchanged2 = [0]*(bal+k+2) 
	for i in range(hs):
		smax = max(arr[i],arr[s-1-i]) + k
		smin = min(arr[i],arr[s-1-i]) + 1 
		unchanged1[smin] += 1 
		unchanged1[smax+1] -= 1
		unchanged2[arr[i]+arr[s-1-i]] += 2 


	for i in range(1,bal+k+2) :
		unchanged1[i] += unchanged1[i-1]  
	for i in range(1,bal+k+1) :
		if(unchanged2[i] > 0) :
			unchanged1[i] += unchanged2[i] // 2
	mans = 0 
	for i in range(1,bal+k+1) :
		mans = max(mans,unchanged1[i],unchanged2[i]) 

	return s-mans





tc = int(input()) 

fun = solve
ans = ""

for ll in range(tc) :
	_,k = map(int,input().split()) 
	li  = [int(x) for x in input().split()] 
	fun(li,_,k)
	ans += "{}\n".format(fun(li,_,k))
print(ans)