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:
def add(arr, N, lo, hi, val): 
    arr[lo] += val 
    if (hi != N - 1): 
        arr[hi + 1] -= val 
  
# Utility method to get actual 
# array from operation array 
def updateArray(arr, N): 
  
    # convert array into prefix sum array 
    for i in range(1, N): 
        arr[i] += arr[i - 1] 
  
# method to print final updated array 
def printArr(arr, N): 
  
    updateArray(arr, N) 
    for i in range(N): 
        print(arr[i]) 
    print()
for _ in range(input()):
    n,k=[int(i) for i in raw_input().split()]
    a=[int(i)-1 for i in raw_input().split()]
    
    arr=[0 for i in range(2*k)]
    d={}
    for i in range(n/2):
        val=a[i]+a[n-1-i]
        d[val]=0
    for i in range(n/2):
        val=a[i]+a[n-1-i]
        d[val]+=1
        minn=min(a[i],a[n-i-1])
        maxx=max(a[i],a[n-i-1])
        add(arr,2*k,0,minn-1,2)
        add(arr,2*k,k+maxx,2*k-1,2)
        add(arr,2*k,minn,k-1+maxx,1)
    updateArray(arr,2*k-1)
    for i in d.keys():
        arr[i]-=d[i]
    arr.pop()
    print(min(arr))