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:
"""T=int(input())
for _ in range(0,T):
    n=int(input())
    a,b=map(int,input().split())
    s=input()
    s=[int(x) for x in input().split()]
    for i in range(0,len(s)):
        a,b=map(int,input().split())"""



T=int(input())
for _ in range(0,T):
    n,k=map(int,input().split())
    s=[int(x) for x in input().split()]
    dp=[0]*((2*k)+5)
    tt=[0]*((2*k)+5)
    for i in range(n//2):
        a=min(s[i],s[n-i-1])
        b=max(s[i],s[n-i-1])
        low=a+1
        high=min(b+k,2*k)
        dp[low]+=1
        dp[high+1]-=1

        dp[2]+=2
        dp[low]-=2
        dp[high+1]+=2
        dp[(2*k)+1]-=2

        tt[a+b]-=1

    ans=(2*n)
    for i in range(3,len(dp)):
        dp[i]+=dp[i-1]

    for i in range(2,(2*k)+1):
        ans=min(ans,dp[i]+tt[i])

    print(ans)

    



        
    """low=2
    high=(2*k)
    ans=n//2
    while(low<=high):
        mid=(low+high)>>1
        r=0
        for i in range(0,n//2):
            if(s[i]>=mid and s[n-i-1]>=mid):
                r+=2
            else:
                r+=1
        ans=min(ans,r)
    print(ans)"""