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:
t = int(input())
for _ in range(t):
    n,k = list(map(int,input().split()))
    a = list(map(int,input().split()))
    b,c = [0]*((2*k)+1),[0]*((2*k)+1)
    i = 0
    d = []
    while i<(n//2):
        p = a[i]+a[n-1-i]
        b[p]+=1
        q = min(a[i],a[n-1-i])+1
        r = max(a[i],a[n-1-i])+k
        if r==(2*k):
            c[q]+=1
        else:
            c[q]+=1
            c[r+1]-=1
        i+=1
    p = (2*k)+1
    for i in range(1,p):
        c[i]=c[i-1]+c[i]
    for i in range(2,p):
        q = b[i]
        r = c[i]
        l = (r-q)+((n//2)-r)*2
        d.append(l)
    print(min(d))