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:
import sys,bisect
input = sys.stdin.readline
from collections import defaultdict
############ ---- USER DEFINED INPUT FUNCTIONS ---- ############
def inp():
    return(int(input().rstrip()))
def inlt():
    return(list(map(int,input().rstrip().split())))
def insr():
    s = input().rstrip()
    return(s[:len(s) - 1])
def invr():
    return(map(int,input().rstrip().split()))
################################################################
############ ---- THE ACTUAL CODE STARTS BELOW ---- ############
def right_index(left):
    return n - left - 1

t = inp()
for _ in range(t):
    n,k = invr()
    nums = inlt()
    right = max(nums) + k + 1
    zero_dict = defaultdict(int)
    mid = n//2;m = 0
    while m < mid:
        result = nums[m] + nums[right_index(m)]
        zero_dict[result] += 1
        m += 1
    ans = [0 for i in range(right + 1)]
    pref = [0 for i in range(right + 1)]
    for i in range(mid):
        left,rightt = nums[i],nums[right_index(i)]
        lindex,rindex = min(left,rightt) + 1, max(left,rightt) + k
        #print(i,lindex,rindex)
        ans[lindex] += 1
        ans[rindex + 1] -= 1

    pref[0] = ans[0]
    for i in range(1,right + 1):
        pref[i] = pref[i - 1] + ans[i]
    min_ans = 100000000
    for i in range(1,right + 1):
        result = n - pref[i] - zero_dict[i]
        if result < min_ans:
            min_ans = result

    print(min_ans)