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:
# -*- coding:utf-8 -*-

"""

created by shuangquan.huang at 2020/6/19

"""

import collections
import time
import os
import sys
import bisect
import heapq
from typing import List


def solve(N, K, A):
    
    M = 2 * K + 1
    x = [0 for _ in range(M)]
    
    add = [0 for _ in range(M)]
    minus = [0 for _ in range(M)]
    wc = collections.defaultdict(int)
    for i in range(N//2):
        a, b = A[i], A[N-i-1]
        wc[a+b] += 1
        s, t = min(a, b) + 1, max(a, b) + K + 1
        if s < M:
            add[s] += 1
        if t < M:
            minus[t] += 1
    
    s = 0
    for i in range(M):
        s += add[i]
        s -= minus[i]
        x[i] = s
        
    ans = N
    for target in range(2, M):
        one = x[target] - wc[target]
        two = N//2-wc[target]-one
        ans = min(ans, one + 2 * two)
        
    return ans
        
        
if __name__ == '__main__':
    T = int(input())
    ans = []
    for ti in range(T):
        N, K = map(int, input().split())
        A = [int(x) for x in input().split()]
        ans.append(solve(N, K, A))
    
    print('\n'.join(map(str, ans)))