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:
"""Template for Python Competitive Programmers prepared by Mayank Chaudhary """

# to use the print and division function of Python3
from __future__ import division, print_function

"""value of mod"""
MOD = 998244353
mod = 10**9 + 7

"""use resource"""
# import resource
# resource.setrlimit(resource.RLIMIT_STACK, [0x100000000, resource.RLIM_INFINITY])

"""for factorial"""

# def prepare_factorial():
#     fact = [1]
#     for i in range(1, 2005):
#         fact.append((fact[-1] * i) % mod)
#     ifact = [0] * 2005
#     ifact[2004] = pow(fact[2004], mod - 2, mod)
#     for i in range(2004, 0, -1):
#         ifact[i - 1] = (i * ifact[i]) % mod
#
#     return fact, ifact

"""uncomment next 4 lines while doing recursion based question"""
import threading
threading.stack_size(1<<27)
import sys
sys.setrecursionlimit(10000)


"""uncomment modules according to your need"""
# from bisect import bisect_left, bisect_right, insort
# import itertools
# from math import floor, ceil, sqrt, degrees, atan, pi, log
# from heapq import heappop, heapify, heappush
# from random import randint as rn
# from Queue import Queue as Q
from collections import Counter, defaultdict, deque
# from copy import deepcopy
'''
def modinv(n, p):
    return pow(n, p - 2, p)
'''

#
# def ncr(n, r,  fact, ifact):  # for using this uncomment the lines calculating fact and ifact
#     t = (fact[n] * (ifact[r]*ifact[n-r]) % mod)% mod
#     return t



def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def input(): return sys.stdin.readline().strip()

"""*****************************************************************************************"""

# def GCD(x, y):
#     while (y):
#         x, y = y, x % y
#     return x

# def lcm(x, y):
#     return (x*y)//(GCD(x, y))

# def get_xor(n):
#     return [n,1,n+1,0][n%4]

# def pow(a, b, d):
#     # print(a, b, d)
#     res = 1
#     while b:
#         if b&1:
#             res = (res%d * a%d)%d
#             b -= 1
#         else:
#             a = (a%d * a%d)%d
#             b>>=1
#
#     return res

""" ********************************************************************************************* """

def main():

    T = int(input())
    while T:
        n, k = get_ints()
        Arr = get_array()

        prefix = [0]*(2*k + 10)
        mydict = {i: 0 for i in range(2*k+2)}
        for i in range(n//2):
            total = Arr[i] + Arr[n-i-1]
            mydict[total] = mydict.get(total, 0)+1

            mini = min(Arr[i], Arr[n-i-1])+1
            maxi = max(Arr[i], Arr[n-i-1])+k
            prefix[mini] += 1
            prefix[maxi+1] -= 1

        for i in range(1, 2*k+10):
            prefix[i] += prefix[i-1]

        ans = n
        for i in range(2, 2*k+1):
            count_0 = mydict[i]
            count_1 = prefix[i] - count_0
            count_2 = n//2 - count_1 - count_0

            ans = min(ans, 2*count_2 + count_1)

        print(ans)
        T-=1


""" -------- Python 2 and 3 footer by Pajenegod and c1729 ---------"""

py2 = round(0.5)
if py2:
    from future_builtins import ascii, filter, hex, map, oct, zip

    range = xrange

import os, sys
from io import IOBase, BytesIO

BUFSIZE = 8192


class FastIO(BytesIO):
    newlines = 0

    def __init__(self, file):
        self._file = file
        self._fd = file.fileno()
        self.writable = "x" in file.mode or "w" in file.mode
        self.write = super(FastIO, self).write if self.writable else None

    def _fill(self):
        s = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
        self.seek((self.tell(), self.seek(0, 2), super(FastIO, self).write(s))[0])
        return s

    def read(self):
        while self._fill(): pass
        return super(FastIO, self).read()

    def readline(self):
        while self.newlines == 0:
            s = self._fill();
            self.newlines = s.count(b"\n") + (not s)
        self.newlines -= 1
        return super(FastIO, self).readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.getvalue())
            self.truncate(0), self.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        if py2:
            self.write = self.buffer.write
            self.read = self.buffer.read
            self.readline = self.buffer.readline
        else:
            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')

# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')

""" main function"""

if __name__ == '__main__':
    # main()
    threading.Thread(target=main).start()