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 int64_t INF = (int64_t)(2e18);
const int inf = (int)(1e9 + 7);
const int maxn = 500 * 1000 + 100;
vector<int> res;
vector<int> vec;
set<pair<int, int>> s;
void go(int i) {
  int tmpi = vec[i];
  int tmpi1 = vec[i + 1];
  int tmpi2 = vec[i + 2];
  s.erase({vec[i], i});
  s.erase({vec[i + 1], i + 1});
  s.erase({vec[i + 2], i + 2});
  s.insert({vec[i], i + 1});
  s.insert({vec[i + 1], i + 2});
  s.insert({vec[i + 2], i});
  vec[i] = tmpi2;
  vec[i + 1] = tmpi;
  vec[i + 2] = tmpi1;
  res.push_back(i);
}
vector<int> myarr;
void solve() {
  res.clear();
  int n;
  cin >> n;
  myarr.resize(n);
  for (auto& it : myarr) cin >> it;
  map<int, vector<int>> lst;
  for (int i = 0; i < n; ++i) lst[myarr[i]].push_back(i);
  vec.resize(n);
  s.clear();
  for (int i = 0; i < n; ++i) s.insert({myarr[i], i});
  int index = 0;
  for (auto& it : s) vec[it.second] = index++;
  int num_inversions = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = i + 1; j < n; ++j)
      if (vec[i] > vec[j]) num_inversions++;
  }
  if (num_inversions % 2 == 1) {
    bool ok = false;
    for (auto& it : lst) {
      if (it.second.size() > 1) {
        swap(vec[it.second[0]], vec[it.second[1]]);
        ok = true;
        break;
      }
    }
    if (!ok) return void(cout << (-1) << endl);
  }
  s.clear();
  for (int i = 0; i < n; ++i) s.insert({vec[i], i});
  int curi = 0;
  while (curi != n - 2) {
    auto cur = *s.begin();
    if (cur.second == curi) {
      curi++;
      s.erase(s.begin());
      continue;
    }
    if (cur.second == curi + 1) {
      go(curi);
      continue;
    }
    go(cur.second - 2);
  }
  for (int i = 0; i < 5; ++i) {
    if (vec[n - 3] <= vec[n - 2] && vec[n - 2] <= vec[n - 1]) break;
    go(n - 3);
    if (i == 4) return void(cout << (-1) << endl);
  }
  cout << res.size() << endl;
  for (auto& it : res) cout << it + 1 << " ";
  cout << endl;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  cin.tie(nullptr);
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}