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 _t in range(t):
    n, k = map(int, input().strip().split())
    a = [int(x) for x in input().split()]
    ref, intvls = dict(), []
    for i in range(n//2):
        x = a[i]+a[n-i-1]
        ref[x] = ref.get(x, 0) + 1
        intvls += [(min(a[i], a[n-i-1])+1, max(a[i], a[n-i-1])+k)]
    # print(ref)
    # print(intvls)
    ff = [0]*2*(k+1)
    for i, j in intvls:
        ff[i] += 1 
        ff[j+1] += -1
        
    ans = 10**9
    for i in range(2, 2*k+1):
        ff[i] += ff[i-1]
        no_of_0s, no_of_1s = ref.get(i, 0), ff[i]-ref.get(i, 0)
        no_of_2s = n//2 - no_of_1s - no_of_0s
        # print(i, ": ", no_of_2s*2 + no_of_1s*1 + no_of_0s*0)
        ans = min(ans, no_of_2s*2 + no_of_1s*1 + no_of_0s*0)
    print(ans)