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 sys
input = lambda: sys.stdin.readline().rstrip("\r\n")

from math import log2


class SegmentTree:
    def __init__(self, array):
        self.n = len(array)
        self.size = 2**(int(log2(self.n-1))+1)
        self.default = 0
        self.data = [self.default] * (2 * self.size)
        self.process(array)

    def process(self, array):
        self.data[self.size : self.size+self.n] = array

    def query(self, index):
        """Returns the value at given index!"""
        res = self.default
        index += self.size
        while index:
            res += self.data[index]
            index >>= 1
        return res

    def update(self, alpha, omega, value):
        """Increases all elements in the range (inclusive) by given value!"""
        alpha += self.size
        omega += self.size + 1
        while alpha < omega:
            if alpha & 1:
                self.data[alpha] += value
                alpha += 1
            if omega & 1:
                omega -= 1
                self.data[omega] += value
            alpha >>= 1
            omega >>= 1

for _ in range(int(input())):
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    i, j = 0, n - 1
    arr = [0] * (2 * k + 1)
    st = SegmentTree(arr)
    di = {}
    while i < j:
        mi, ma = min(a[i], a[j]), max(a[i], a[j])
        s = str(mi) + "," + str(ma)
        di[s] = 1 if s not in di else di[s] + 1
        i += 1
        j -= 1
    for each in di:
        mi, ma = [int(k) for k in each.split(",")]
        total = mi + ma
        st.update(0, mi, 2 * di[each])
        st.update(mi + 1, total - 1, 1 * di[each])
        if total != 2 * k:
            st.update(total + 1, ma + k, 1 * di[each])
        if ma != k:
            st.update(ma + k + 1, 2 * k, 2 * di[each])

    print(min([st.query(k) for k in range(2 * k + 1)]))