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 int N = 505;
int va[N];
vector<int> v;
inline void update(int i, int j) {
  if (i - j > 1) {
    int tep = va[i];
    va[i] = va[i - 1];
    va[i - 1] = va[i - 2];
    va[i - 2] = tep;
    v.push_back(i - 2);
    i -= 2;
    if (i != j) update(i, j);
  } else {
    v.push_back(j);
    v.push_back(j);
    int vj = va[j], vi = va[i];
    va[i] = va[i + 1];
    va[j] = vi;
    va[i + 1] = vj;
  }
}
int main() {
  ios::sync_with_stdio(false);
  int t;
  cin >> t;
  while (t--) {
    v.clear();
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> va[i];
    bool ff = 0;
    for (int i = 1; i <= n - 2; i++) {
      int pos = i;
      for (int j = i; j <= n; j++)
        if (va[pos] > va[j]) pos = j;
      if (i != pos) update(pos, i);
    }
    for (int i = n - 2; i >= 1; i--) {
      int fi = 1;
      for (int j = 1; j < n; j++)
        if (va[j] > va[j + 1]) {
          fi = 0;
          break;
        }
      if (fi) {
        ff = 1;
        break;
      }
      v.push_back(i);
      int tmp = va[i + 2];
      va[i + 2] = va[i + 1];
      va[i + 1] = va[i];
      va[i] = tmp;
    }
    int fi = 1;
    for (int j = 1; j < n; j++)
      if (va[j] > va[j + 1]) {
        fi = 0;
        break;
      }
    if (fi) ff = 1;
    if (!ff)
      cout << "-1" << endl;
    else {
      cout << v.size() << endl;
      for (int i = 0; i < v.size(); i++) {
        if (i != 0) cout << " ";
        cout << v[i];
      }
      cout << endl;
    }
  }
}