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;
int main() {
  auto make = [](vector<int> &a, int pos) {
    swap(a[pos + 1], a[pos + 2]);
    swap(a[pos], a[pos + 1]);
  };
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    vector<int> a(n);
    vector<pair<int, int>> res(n);
    for (int i = 0; i < n; ++i) {
      cin >> a[i];
      res[i] = {a[i], i};
    }
    sort(res.begin(), res.end());
    for (int i = 0; i < n; ++i) {
      a[res[i].second] = i;
    }
    int cnt = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = i + 1; j < n; ++j) {
        cnt += a[j] < a[i];
      }
    }
    if (cnt & 1) {
      for (int i = 0; i < n - 1; ++i) {
        if (res[i].first == res[i + 1].first) {
          swap(a[res[i].second], a[res[i + 1].second]);
          break;
        }
      }
    }
    vector<int> ans;
    for (int i = 0; i < n - 2; ++i) {
      int pos = min_element(a.begin() + i, a.end()) - a.begin();
      while (pos > i + 1) {
        make(a, pos - 2);
        ans.push_back(pos - 2);
        pos -= 2;
      }
      if (pos != i) {
        make(a, i);
        make(a, i);
        ans.push_back(i);
        ans.push_back(i);
        pos = i;
      }
    }
    for (int i = 0; i < 3; ++i) {
      if (is_sorted(a.begin(), a.end())) {
        break;
      }
      make(a, n - 3);
      ans.push_back(n - 3);
    }
    if (!is_sorted(a.begin(), a.end())) {
      cout << -1 << endl;
    } else {
      cout << ans.size() << endl;
      for (auto it : ans) cout << it + 1 << " ";
      cout << endl;
    }
  }
  return 0;
}