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:
FAST_IO = 1
if FAST_IO:
    import io, sys, atexit
    rr = iter(sys.stdin.read().splitlines()).next
    sys.stdout = _OUTPUT_BUFFER = io.BytesIO()
    @atexit.register
    def write():
        sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
else:
    rr = raw_input
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())


from collections import Counter, defaultdict as ddic
def solve(N, K, A):
    # N even, all ai <= K
    # replace minimum elements so ai + a~i = x
    N2 = N // 2
    count = [0] * (2*K + 2)
    for i in xrange(N2):
        x = A[i]
        y = A[~i]
        if x>y:x,y=y,x
        s = x + y
        # all s  in [a+1, b+K] is 1
        # rest is 0
        # s == a+b is 2
        count[x+1] += 1  # 
        count[y+K+1] -= 1
        count[s] += 1
        count[s+1] -= 1
        
    for i in xrange(1,2*K+2):
        count[i] += count[i-1]
    #print("!", count)
    return 2 * N2 - max(count)
        
        
        

T = rri()
for t in xrange(1, T+1):
    N,K =rrm()
    A = rrm()
    ans= solve(N, K, A)
    print ans