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;
vector<string> vec_splitter(string s) {
  s += ',';
  vector<string> res;
  while (!s.empty()) {
    res.push_back(s.substr(0, s.find(',')));
    s = s.substr(s.find(',') + 1);
  }
  return res;
}
void debug_out(vector<string> __attribute__((unused)) args,
               __attribute__((unused)) int idx,
               __attribute__((unused)) int LINE_NUM) {
  cerr << endl;
}
template <typename Head, typename... Tail>
void debug_out(vector<string> args, int idx, int LINE_NUM, Head H, Tail... T) {
  if (idx > 0)
    cerr << ", ";
  else
    cerr << "Line(" << LINE_NUM << ") ";
  stringstream ss;
  ss << H;
  cerr << args[idx] << " = " << ss.str();
  debug_out(args, idx + 1, LINE_NUM, T...);
}
template <class T>
bool ckmin(T& a, T& b) {
  bool r = a > b;
  a = min(a, b);
  return r;
}
template <class T>
bool ckmax(T& a, T& b) {
  bool r = a < b;
  a = max(a, b);
  return r;
}
const int MOD = 1e9 + 7;
const long long INF = 1e18;
int mini(vector<int>& a, int l) {
  int ret = l;
  int v = a[l];
  for (int i = l + 1; i < a.size(); i++) {
    if (ckmin(v, a[i])) {
      ret = i;
    }
  }
  return ret;
}
void op(vector<int>& ans, int i, vector<int>& a) {
  ans.push_back(i);
  int x = a[i];
  int y = a[i + 1];
  int z = a[i + 2];
  a[i] = z;
  a[i + 1] = x;
  a[i + 2] = y;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int T;
  cin >> T;
  while (T--) {
    int n;
    cin >> n;
    vector<pair<int, int> > a(n);
    for (int i = 0; i < n; i++) {
      cin >> a[i].first;
      a[i].second = i;
    }
    vector<int> ans;
    int inv = 0;
    bool eq = false;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < i; j++) {
        if (a[j].first > a[i].first) {
          inv++;
        }
        if (a[j].first == a[i].first) {
          eq = true;
        }
      }
    }
    if ((inv & 1) && !eq) {
      cout << "-1\n";
      continue;
    }
    sort(begin(a), end(a));
    if (inv & 1) {
      for (int i = 0; i < n - 1; i++) {
        if (a[i].first == a[i + 1].first) {
          swap(a[i], a[i + 1]);
          break;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      42;
    }
    vector<int> na(n);
    for (int i = 0; i < n; i++) {
      na[a[i].second] = i;
    }
    for (int i = 0; i < n - 2; i++) {
      int v = mini(na, i);
      while (v - 2 >= i) {
        op(ans, v - 2, na);
        v -= 2;
      }
      if (v - 1 == i) {
        op(ans, i, na);
        op(ans, i, na);
      }
    }
    for (int i = 0; i < n; i++) {
      42;
    }
    cout << ans.size() << '\n';
    ;
    for (auto& v : ans) cout << v + 1 << " ";
    cout << '\n';
    ;
  }
}