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;
using cd = complex<double>;
const long long INF = 1e15;
const int N = 3e5 + 2;
const int mod = 1e9 + 7;
const double Pi = acos(-1);
void Fastio() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
}
int t;
int n;
int a[505];
vector<int> Ans;
void Move(int id) {
  int temp = a[id + 2];
  a[id + 2] = a[id + 1];
  a[id + 1] = a[id];
  a[id] = temp;
}
void Solve() {
  cin >> n;
  Ans.clear();
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n - 2; j++) {
      if (a[j] > a[j + 1]) {
        Move(j);
        Ans.emplace_back(j);
        Move(j);
        Ans.emplace_back(j);
      } else if (a[j + 1] > a[j + 2]) {
        Move(j);
        Ans.emplace_back(j);
      }
    }
  }
  for (int i = 1; i < n; i++) {
    if (a[i] > a[i + 1]) {
      cout << -1 << '\n';
      return;
    }
  }
  cout << Ans.size() << '\n';
  for (auto x : Ans) {
    cout << x << ' ';
  }
  cout << '\n';
}
signed main() {
  Fastio();
  cin >> t;
  while (t--) {
    Solve();
  }
}