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>
#pragma warning(disable : 4996)
#pragma comment(linker, "/STACK:16777216")
using namespace std;
const int INF = 2000000000;
const long long LINF = 2000000000000000000;
template <typename T>
void print(vector<T>& a) {
  for (int i = 0; i < a.size(); i++) cout << a[i] << ' ';
  cout << '\n';
}
template <typename T>
void print(deque<T>& a) {
  for (int i = 0; i < a.size(); i++) cout << a[i] << ' ';
  cout << '\n';
}
template <typename T>
void print(vector<vector<T>>& a) {
  for (int i = 0; i < a.size(); i++) {
    for (int j = 0; j < a[i].size(); j++) cout << a[i][j] << ' ';
    cout << '\n';
  }
}
template <typename T>
void input(vector<T>& a) {
  for (int i = 0; i < a.size(); i++) cin >> a[i];
}
template <typename T>
void input(deque<T>& a) {
  for (int i = 0; i < a.size(); i++) cin >> a[i];
}
template <typename T>
void input(vector<vector<T>>& a) {
  for (int i = 0; i < a.size(); i++)
    for (int j = 0; j < a[i].size(); j++) cin >> a[i][j];
}
vector<int> ans;
void change(vector<int>& a, int idx) {
  int t = a[idx + 2];
  a[idx + 2] = a[idx + 1];
  a[idx + 1] = a[idx];
  a[idx] = t;
}
void solve() {
  ans.clear();
  int n;
  cin >> n;
  vector<int> a(n);
  input(a);
  if (n == 3) {
    for (int j = 0; j < 4; j++)
      if (is_sorted((a).begin(), (a).end())) {
        cout << j << '\n';
        for (int k = 0; k < j; k++) cout << 1 << ' ';
        cout << '\n';
        return;
      } else
        change(a, 0);
    cout << -1 << '\n';
    return;
  }
  for (int i = 0; i < n - 2; i++) {
    int idx = i;
    for (int j = i; j < n; j++) {
      if (a[j] < a[idx]) idx = j;
    }
    while (idx > i) {
      if (idx - 2 >= i) {
        change(a, idx - 2);
        ans.push_back(idx - 2);
        idx -= 2;
      } else {
        change(a, idx - 1);
        ans.push_back(idx - 1);
        change(a, idx - 1);
        ans.push_back(idx - 1);
        idx--;
      }
    }
  }
  if (is_sorted((a).begin(), (a).end())) {
    cout << ans.size() << '\n';
    for (auto to : ans) cout << to + 1 << ' ';
    cout << '\n';
  } else {
    if (a[n - 1] == a[n - 3]) {
      ans.push_back(n - 3);
      cout << ans.size() << '\n';
      for (auto to : ans) cout << to + 1 << ' ';
      cout << '\n';
      return;
    }
    int num = -1;
    int idx = -1;
    for (int i = 1; i < n; i++) {
      if (a[i] == a[i - 1]) {
        num = a[i];
        idx = i;
      }
    }
    if (num == -1) {
      cout << -1 << '\n';
      return;
    }
    for (int i = n - 1; i > idx; i--) {
      change(a, i - 2);
      ans.push_back(i - 2);
    }
    cout << ans.size() << '\n';
    for (auto to : ans) cout << to + 1 << ' ';
    cout << '\n';
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int tst = 1;
  cin >> tst;
  while (tst--) solve();
}