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 collections import deque
t=int(input())
def inc(n,arr,l,r):
    if(l<=r and l>=0):
        arr[l]+=n
        if(r+1<=len(arr)-1):
            arr[r+1]-=n


for i1 in range(t):
    n,k=list(map(int,input().split(" ")))
    l1=list(map(int,input().split(" ")))
    arr=[0]*(2*k+1)
    for i in range(n//2):
        z1=l1[i]
        z2=l1[n-i-1]
        s=z1+z2
        min1=min(z1,z2)
        max1=max(z1,z2)
        if(s!=2*k):
            l,r=s+k-min1+1,2*k
            inc(2,arr,l,r)
            
            l,r=s+1,s+k-min1
            inc(1,arr,l,r)

        l,r=s-(max1-1),s-1  
        inc(1,arr,l,r)

        l,r=0,s-(max1-1)-1 
        inc(2,arr,l,r) 
    for i in range(1,len(arr)):
        arr[i]+=arr[i-1]
    # print(arr)
    print(min(arr))