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;
template <class T>
void Output(const T& v, bool print_new_line = true) {
  bool first = true;
  for (auto element : v) {
    if (!first)
      cout << " ";
    else
      first = false;
    cout << element;
  }
  if (print_new_line) cout << endl;
}
template <class T>
void Input(vector<T>& v, int n) {
  v.resize(n);
  for (int i = 0; i < n; ++i) {
    cin >> v[i];
  }
}
template <class T>
vector<int> Query(const T& c, int answer_counts) {
  cout << "? " << c.size();
  for (auto it = c.begin(); it != c.end(); ++it) {
    cout << " " << (*it);
  }
  cout << endl;
  cout.flush();
  vector<int> s(answer_counts);
  for (int i = 0; i < answer_counts; ++i) {
    cin >> s[i];
  }
  return s;
}
void shift(vector<int>& a, int k, vector<int>* ans, int* reverse) {
  if (ans) ans->push_back(k + 1);
  if (reverse) {
    *reverse -= (int)(a[k] > a[k + 1]) + (int)(a[k] > a[k + 2]) +
                (int)(a[k + 1] > a[k + 2]);
  }
  int t = a[k + 2];
  a[k + 2] = a[k + 1];
  a[k + 1] = a[k];
  a[k] = t;
  if (reverse) {
    *reverse += (int)(a[k] > a[k + 1]) + (int)(a[k] > a[k + 2]) +
                (int)(a[k + 1] > a[k + 2]);
  }
}
int main() {
  int case_number;
  cin >> case_number;
  for (int case_index = 0; case_index < case_number; ++case_index) {
    int n;
    vector<int> a;
    cin >> n;
    Input(a, n);
    if (n == 3) {
      int ct = 0;
      while ((a[0] > a[1] || a[1] > a[2]) && ct <= 2) {
        ++ct;
        shift(a, 0, nullptr, nullptr);
      }
      if (ct > 2)
        cout << -1 << endl;
      else {
        cout << ct << endl;
        for (int i = 0; i < ct; ++i) cout << "1 ";
        cout << endl;
      }
      continue;
    }
    int least_dup = -1;
    int reverse = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < i; ++j) {
        if (a[j] > a[i]) ++reverse;
        if (a[j] == a[i] && (least_dup == -1 || least_dup > a[i])) {
          least_dup = a[i];
        }
      }
    }
    if (reverse % 2 != 0 && least_dup == -1) {
      cout << -1 << endl;
      continue;
    }
    vector<int> ans;
    for (int i = n - 1; i >= 0; --i) {
      int largest = 0;
      for (int j = 1; j <= i; ++j) {
        if (a[largest] <= a[j]) {
          largest = j;
        }
      }
      if (reverse % 2 == 1 && a[largest] < least_dup && i < n - 1 &&
          a[i + 1] == least_dup) {
        shift(a, i, &ans, &reverse);
        shift(a, i - 1, &ans, &reverse);
        ++i;
        continue;
      }
      if (i >= 2) {
        while (largest + 2 <= i) {
          shift(a, largest, &ans, &reverse);
          ++largest;
        }
        if (largest + 1 == i) {
          shift(a, largest - 1, &ans, &reverse);
        }
      }
    }
    while (reverse != 0) {
      shift(a, 0, &ans, &reverse);
    }
    cout << ans.size() << endl;
    Output(ans);
  }
  return 0;
}