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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t, n;
  cin >> t;
  while (t--) {
    cin >> n;
    vector<pair<int, int>> b(n), a(n);
    for (int i = 0; i < n; i++) {
      cin >> a[i].first;
      a[i].second = i;
    }
    sort(a.begin(), a.end());
    for (int i = 0; i < n; i++) {
      b[a[i].second].first = a[i].first;
      b[a[i].second].second = i;
    }
    int inv = 0;
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (b[i].second > b[j].second) {
          inv++;
        }
      }
    }
    bool ok = true;
    if (inv % 2) {
      bool found = false;
      for (int i = 0; i < n - 1; i++) {
        if (a[i].first == a[i + 1].first) {
          swap(b[a[i].second], b[a[i + 1].second]);
          found = true;
          break;
        }
      }
      if (!found) {
        ok = false;
      }
    }
    if (!ok) {
      cout << "-1\n";
    } else {
      vector<int> ans;
      for (int i = 0; i < n; i++) {
        if (b[i].second == i) {
          continue;
        } else {
          for (int j = 0; j < n; j++) {
            if (b[j].second == i) {
              int k = j;
              while (i < k) {
                if (k - 2 < i) {
                  swap(b[k - 1], b[k + 1]);
                  ans.push_back(k - 1);
                  swap(b[k], b[k + 1]);
                  swap(b[k - 1], b[k + 1]);
                  ans.push_back(k - 1);
                  swap(b[k], b[k + 1]);
                  k--;
                } else {
                  swap(b[k - 2], b[k]);
                  ans.push_back(k - 2);
                  swap(b[k - 1], b[k]);
                  k -= 2;
                }
              }
              break;
            }
          }
        }
      }
      if (!ok) {
        cout << "-1\n";
      } else {
        cout << ans.size() << "\n";
        for (auto a : ans) {
          cout << a + 1 << " ";
        }
        cout << "\n";
      }
    }
  }
  return 0;
}