Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 1e4 + 10;
const int inf = 1e9;
const int mo = 998244353;
int a[N], b[N];
void trans(int i) {
  swap(a[i], a[i + 2]);
  swap(a[i + 1], a[i + 2]);
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    vector<int> ans;
    int n;
    cin >> n;
    for (auto i = (1); i <= (n); ++i) cin >> a[i];
    for (auto i = (1); i <= (n); ++i) b[i] = a[i];
    sort(b + 1, b + 1 + n);
    int mepos = -1;
    for (auto i = (2); i <= (n); ++i) {
      if (b[i] == b[i - 1]) mepos = i;
    }
    bool ok = 1;
    for (auto i = (1); i <= (n); ++i) {
      int now = b[i];
      for (auto j = (i); j <= (n); ++j) {
        if (a[j] == now) {
          for (int k = j - 2; k >= i; k -= 2) {
            ans.push_back(k);
            trans(k);
          }
        }
      }
      if (a[i] != now) {
        if (i + 2 <= n) {
          ans.push_back(i);
          trans(i);
          ans.push_back(i);
          trans(i);
        } else
          ok = 0;
      }
      if (i == mepos) {
        int inv = 0;
        for (auto j = (i + 2); j <= (n); ++j) {
          for (auto k = (i + 1); k <= (j - 1); ++k) {
            if (a[k] > a[j]) inv++;
          }
        }
        if (inv & 1) {
          trans(i - 1);
          trans(i - 1);
          trans(i);
          trans(i);
          ans.push_back(i - 1);
          ans.push_back(i - 1);
          ans.push_back(i);
          ans.push_back(i);
        }
      }
    }
    if (!ok && a[n - 2] == a[n]) {
      ans.push_back(n - 2);
      trans(n - 2);
      ok = 1;
    }
    if (!ok) {
      cout << "-1\n";
    } else {
      cout << ans.size() << endl;
      for (auto x : ans) cout << x << " ";
      cout << endl;
    }
  }
  return 0;
}