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 long long N = 510;
long long a[N];
void rot1(long long& first, long long& second, long long& z) {
  tie(first, second, z) = make_tuple(z, first, second);
}
void rot2(long long ind) { rot1(a[ind], a[ind + 1], a[ind + 2]); }
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    map<long long, long long> pos;
    long long pos1 = 0, pos2 = 0;
    for (long long i = 1; i <= n; i++) {
      cin >> a[i];
      if (pos.count(a[i])) pos1 = pos[a[i]], pos2 = i;
      pos[a[i]] = i;
      a[i] *= N;
      a[i] += i;
    }
    bool even = true;
    for (long long i = 1; i <= n; i++)
      for (long long j = i + 1; j <= n; j++)
        if (a[i] > a[j]) even = !even;
    if (!even)
      if (pos1)
        swap(a[pos1], a[pos2]);
      else {
        cout << -1 << "\n";
        continue;
      }
    vector<long long> idx;
    while (true) {
      long long i = 1;
      while (i <= n && min_element(a + i, a + n + 1) == a + i) i++;
      if (i > n - 2) break;
      long long j = min_element(a + i, a + n + 1) - a;
      while (j - i >= 2) rot2(j - 2), idx.push_back(j - 2), j -= 2;
      if (j - i == 1) rot2(i), idx.push_back(i), rot2(i), idx.push_back(i);
    }
    if (is_sorted(a + 1, a + n + 1)) {
      cout << idx.size() << "\n";
      for (long long i : idx) cout << i << " ";
      cout << "\n";
    } else
      cout << -1 << "\n";
  }
}