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:
A = [0 for x in range(400005)]
t = int(input())
def mymin(a,b):
    if(a<b):
        return a
    else:
        return b

def mymax(a,b):
    if(a>b):
        return a
    else:
        return b

for tests in range(t):
    [n,k] = input().split()
    n = int(n)
    k = int(k)
    B = input().split()
    for i in range(2,(2*k)+1):
        A[i] = 0
    n2 = int(n/2)
    for i in range(n2):
        B[i] = int(B[i])
        B[n-1-i] = int(B[n-1-i])
        mi = mymin(B[i],B[n-1-i])
        ma = mymax(B[i],B[n-1-i])
        A[2] += 2
        A[mi+1] -= 1
        A[mi+ma] -= 1
        if(mi+ma+1 <= 2*k):
            A[mi+ma+1] +=1
        if(ma+k+1 <= 2*k):
            A[ma+k+1] +=1
    ans = n
    for i in range(2,(2*k)+1):
        A[i] += A[i-1]
        if(A[i]<ans):
            ans = A[i]
    print(ans)