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(0);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    vector<int> v(n);
    vector<pair<int, int>> u;
    for (long long i = 0; i < n; i++) {
      cin >> v[i];
      u.push_back({v[i], i});
    }
    sort(u.begin(), u.end());
    for (long long i = 0; i < n; i++) v[u[i].second] = i;
    int inv = 0;
    for (long long i = 0; i < n; i++) {
      for (long long j = i + 1; j < n; j++) {
        if (v[j] < v[i]) inv++;
      }
    }
    if (inv % 2) {
      for (long long i = 0; i < n - 1; i++) {
        if (u[i].first == u[i + 1].first) {
          swap(v[u[i].second], v[u[i + 1].second]);
          break;
        }
      }
    }
    int cnt = 0;
    vector<int> op;
    for (long long i = 0; i < n - 2; i++) {
      int x = v[i], mn = 1e9, pos;
      for (long long j = i + 1; j < n; j++) {
        if (v[j] < mn) {
          mn = v[j];
          pos = j;
        }
      }
      if (mn > x) {
        cnt++;
        continue;
      }
      while (pos > 2 + cnt) {
        op.push_back(pos - 1);
        swap(v[pos], v[pos - 2]);
        swap(v[pos], v[pos - 1]);
        pos -= 2;
      }
      if (pos == 1 + cnt) {
        op.push_back(1 + cnt);
        swap(v[0 + cnt], v[2 + cnt]);
        swap(v[2 + cnt], v[1 + cnt]);
        op.push_back(1 + cnt);
        swap(v[0 + cnt], v[2 + cnt]);
        swap(v[2 + cnt], v[1 + cnt]);
      }
      if (pos == 2 + cnt) {
        op.push_back(1 + cnt);
        swap(v[0 + cnt], v[2 + cnt]);
        swap(v[2 + cnt], v[1 + cnt]);
      }
      cnt++;
    }
    int can = 0;
    for (long long i = 0; i < 4; i++) {
      if (is_sorted(v.begin(), v.end())) {
        can = 1;
        break;
      }
      op.push_back(n - 2);
      swap(v[n - 3], v[n - 1]);
      swap(v[n - 1], v[n - 2]);
    }
    if (!can)
      cout << "-1\n";
    else {
      cout << ((int)(op).size()) << "\n";
      for (auto x : op) cout << x << " ";
      cout << "\n";
    }
  }
  return 0;
}