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 os
import sys
from io import BytesIO, IOBase
 
BUFSIZE = 8192
 
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

import copy

t = int(input())
# 
for _ in range(t):
    n,k = map(int,input().split(' '))

    #x = [int(i) for i in input().split(' ')]
    li = [int(i) for i in input().split(' ')]
    s = {}
    possible = {}
    possible2 = {}
    for i in range(n//2):
        s[li[i]+li[n-i-1]]=s.get(li[i]+li[n-i-1],0)+1
        possible[max(li[i],li[n-1-i])+k] = possible.get(max(li[i],li[n-1-i])+k,0)+1
        possible2[min(li[i],li[n-1-i])+1] = possible2.get(min(li[i],li[n-1-i])+1,0)+1
    pl = sorted(possible)
    pl2 = sorted(possible2)
    sl = sorted(s)
    m = int(1e6)
    pref = 0
    suff = n//2
    
    plidx = 0
    plidx2 = 0
    for i in sl:
        while (plidx<len(pl) and i > pl[plidx]) or (plidx2 <len(pl2) and i >= pl2[plidx2]):
            if plidx2 >= len(pl2):
                m = min(m,n//2+pref-s.get(pl[plidx],0)+suff)
                pref += possible[pl[plidx]]
                plidx+=1
                continue
            elif plidx>=len(pl):
                suff -= possible2[pl2[plidx2]]
                m = min(m,n//2+pref-s.get(pl2[plidx2],0)+suff)
                plidx2+=1
            else:
                if plidx2 <len(pl2) and pl[plidx] > pl2[plidx2]:
                    suff -= possible2[pl2[plidx2]]
                    m = min(m,n//2+pref-s.get(pl2[plidx2],0)+suff)
                    plidx2+=1
                    continue
                elif plidx<len(pl) and pl[plidx] < pl2[plidx2]:
                    m = min(m,n//2+pref-s.get(pl[plidx],0)+suff)
                    pref += possible[pl[plidx]]
                    plidx+=1
                    continue
                else:
                    if not plidx<len(pl) and plidx2 <len(pl2):
                        break
                    suff -= possible2[pl2[plidx2]]
                    m = min(m,n//2+pref-s.get(pl2[plidx2],0)+suff)
                    plidx2+=1
                    pref += possible[pl[plidx]]
                    plidx+=1
        m = min(m,n//2+pref-s[i]+suff)
    print(m)