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 update(bit, l, r, n, val):
    updatebit(bit, n, l, val)
    updatebit(bit, n, r+1, -val)

def updatebit(bit, n, i, val):
    i += 1
    while i <= n:
        bit[i] += val
        i += i & (-i)

def get(bit, i):
    res = 0
    i += 1
    while i > 0:
        res += bit[i]
        i -= i & (-i)
    return res


t = int(input())
for tt in range(t):
    N, K = (int(i) for i in input().split())
    A = [int(i) for i in input().split()]
    pos = [0]*(2*K+2)
    n = len(pos) - 1
    for i in range(N//2):
        cur, mir = A[i], A[N-i-1]
        L = R = cur + mir
        update(pos, L, R, n, -1)
        
        L, R = 2, min(cur, mir)
        if L <= R:
            update(pos, L, R, n, 1)
            
        L, R = max(cur, mir) + K + 1, n - 1
        if L <= R:
            update(pos, L, R, n, 1)
            
    ans = N//2 + min(get(pos, i) for i in range(2, n))
    print(ans)