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;
void solve() {
  int n;
  cin >> n;
  vector<int> a(n + 1);
  for (int i = 1; i <= n; i++) cin >> a[i];
  vector<int> ans;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j < n - 1; j++) {
      if (a[j] > a[j + 1]) {
        swap(a[j], a[j + 2]);
        swap(a[j], a[j + 1]);
        ans.emplace_back(j);
        ans.emplace_back(j);
      } else if (a[j + 1] > a[j + 2]) {
        swap(a[j], a[j + 1]);
        swap(a[j], a[j + 2]);
        ans.emplace_back(j);
      }
    }
  }
  int i;
  for (i = 2; i <= n; i++)
    if (a[i] < a[i - 1]) break;
  if (i <= n) {
    cout << "-1";
  } else {
    cout << ans.size() << "\n";
    for (int aa : ans) cout << aa << " ";
  }
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int q;
  cin >> q;
  while (q--) {
    solve();
    cout << "\n";
  }
}