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 maxn = 2e5 + 5;
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
struct Node {
  int val, pri, ind;
  bool operator<(const Node &o) const {
    return val == o.val ? pri < o.pri : val < o.val;
  }
} b[maxn];
int a[maxn];
int n;
void op(int i) {
  int tmp = a[i + 2];
  a[i + 2] = a[i + 1];
  a[i + 1] = a[i];
  a[i] = tmp;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int t;
  cin >> t;
  while (t--) {
    cin >> n;
    map<int, int> mp;
    int px = 0, py = 0;
    for (int i = 1; i <= n; ++i) {
      cin >> a[i];
      ++mp[a[i]];
      b[i] = {a[i], mp[a[i]], i};
    }
    int cnt = 0;
    for (int i = 1; i <= n; ++i) {
      for (int j = 1; j < i; ++j) {
        if (a[j] > a[i]) ++cnt;
      }
    }
    if (((int)mp.size()) == n && (cnt & 1)) {
      cout << "-1\n";
      continue;
    }
    if (cnt & 1) {
      int val = 0;
      for (auto &it : mp) {
        if (it.second > 1) {
          val = it.first;
          break;
        }
      }
      for (int i = 1; i <= n; ++i) {
        if (b[i].val == val) {
          for (int j = i + 1; j <= n; ++j) {
            if (b[j].val == val) {
              swap(b[j].pri, b[i].pri);
              break;
            }
          }
          break;
        }
      }
    }
    sort(b + 1, b + 1 + n);
    for (int i = 1; i <= n; ++i) {
      a[b[i].ind] = i;
    }
    vector<int> ans;
    for (int i = n; i >= 3; --i) {
      int pmx = 0, mx = 0;
      for (int j = 1; j <= i; ++j) {
        if (!pmx || a[j] > mx) mx = a[j], pmx = j;
      }
      if (pmx == i) continue;
      while (pmx < i - 1) {
        ans.push_back(pmx);
        op(pmx);
        ++pmx;
      }
      ans.push_back(i - 2);
      op(i - 2);
    }
    cout << ((int)ans.size()) << "\n";
    for (auto &v : ans) cout << v << " ";
    cout << "\n";
  }
  return 0;
}