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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
int arr[200005], cnt[400005];
int t, n, k;
void add(int l, int r, int v) {
  if (l > r) return;
  cnt[l] += v;
  cnt[r + 1] -= v;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> t;
  while (t--) {
    cin >> n >> k;
    for (int i = 0; i <= 2 * k; i++) cnt[i] = 0;
    for (int i = 0; i < n; i++) cin >> arr[i];
    for (int i = 0; i < n / 2; i++) {
      int a = min(arr[i], arr[n - i - 1]);
      int b = max(arr[i], arr[n - i - 1]);
      add(2, a, 2);
      add(a + 1, b + k, 1);
      add(a + b, a + b, -1);
      add(b + k + 1, 2 * k, 2);
    }
    int ans = INF;
    for (int i = 2; i <= 2 * k; i++) {
      cnt[i] += cnt[i - 1];
      ans = min(ans, cnt[i]);
    }
    cout << ans << '\n';
  }
  return 0;
}