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 PYTHON):

Solution:
# coding=utf-8
from collections import deque


def main():
    for _ in range(input()):
        n, k = map(int, raw_input().split())
        a = map(int, raw_input().split())
        sum = [0 for _ in range(0, 2 * k + 5)]
        for i in range(0, n / 2):
            val1 = a[i]
            val2 = a[n - 1 - i]
            mi = min(val1, val2)
            mx = max(val1, val2)
            # mi + 1, mx + k
            sum[mi + 1] += 1
            sum[mx + k + 1] -= 1
            sum[val1 + val2] -= 1
            sum[val1 + val2 + 1] += 1
            # print sum
            # 2 mi + 1
            if 2 <= mi:
                sum[2] += 2
                sum[mi + 1] -= 2
            # print sum
            # mx+k+1 2*k
            if mx + k + 1 <= 2 * k:
                sum[mx + k + 1] += 2
                sum[2 * k + 1] -= 2
            # print sum
            # print "ssssssssss"
        ans = n + 5
        for i in range(2, 2 * k + 1):
            sum[i] += sum[i - 1]
            # print i, sum[i]
            ans = min(ans, sum[i])
        print ans


if __name__ == "__main__":
    main()

"""
4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4

"""