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
input=sys.stdin.readline
from math import *
import bisect as bs
t=int(input())
while t>0:
    t-=1
    n,k=map(int,input().split())
    a=[int(x) for x in input().split()]
    d=[0 for i in range(2*k+2)]
    for i in range(n//2):
        c=min(a[i],a[n-i-1])
        dd=max(a[i],a[n-i-1])
        maxi=a[i]+a[n-i-1]+k-c
        mini=a[i]+a[n-i-1]-dd+1
        #print(mini,maxi,a[i],a[n-i-1])
        d[mini]+=1
        d[a[i]+a[n-i-1]]-=1
        d[a[i]+a[n-i-1]+1]+=1
        d[maxi+1]-=1
        if mini>2:
            d[2]+=2
            d[mini]-=2
        if maxi<2*k:
            d[maxi+1]+=2
            d[2*k+1]-=2
        #print(d)    
    for i in range(1,len(d)):
        d[i]+=d[i-1]
    #print("Final",d)    
    print(min(d[2:2*k+1]))