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;
long long int pos(long long int n) {
  if (n >= 0) {
    return n;
  }
  return -n;
}
long long int gcd(long long int a, long long int b) {
  if (a == 0) {
    return b;
  }
  return gcd(b % a, a);
}
signed main() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    vector<long long int> v;
    v.push_back(0);
    vector<long long int> a;
    a.push_back(0);
    for (long long int i = 1; i <= n; i++) {
      long long int z;
      cin >> z;
      v.push_back(z);
      a.push_back(z);
    }
    sort(a.begin(), a.end());
    vector<long long int> moves;
    long long int next = n;
    while (next >= 3) {
      for (long long int i = 1; i <= n; i++) {
        if (v[i] == a[next]) {
          if (i == 1) {
            moves.push_back(1);
            long long int x = v[3];
            v[3] = v[2];
            v[2] = v[1];
            v[1] = x;
            x = v[2 - 1];
            long long int y = v[2];
            for (long long int j = 2 - 1; j <= next - 2; j++) {
              moves.push_back(j);
            }
            for (long long int j = 2 - 1; j <= next - 2; j++) {
              v[j] = v[j + 2];
            }
            v[next - 1] = x;
            v[next] = y;
          } else {
            long long int x = v[i - 1];
            long long int y = v[i];
            for (long long int j = i - 1; j <= next - 2; j++) {
              moves.push_back(j);
            }
            for (long long int j = i - 1; j <= next - 2; j++) {
              v[j] = v[j + 2];
            }
            v[next - 1] = x;
            v[next] = y;
          }
          next--;
          break;
        }
      }
    }
    long long int dup = 0;
    for (long long int i = 2; i <= n - 1; i++) {
      if (v[i] == v[i + 1]) {
        dup = i;
        break;
      }
    }
    if (v[1] == a[1]) {
      cout << moves.size() << endl;
      for (long long int i = 0; i < moves.size(); i++) {
        cout << moves[i] << " ";
      }
      cout << "\n";
      continue;
    }
    if (dup == 0) {
      if (v[1] == v[3]) {
        moves.push_back(1);
        moves.push_back(1);
        cout << moves.size() << endl;
        for (long long int i = 0; i < moves.size(); i++) {
          cout << moves[i] << " ";
        }
        cout << "\n";
        continue;
      }
      cout << "-1\n";
      continue;
    }
    if (dup % 2 == 1) {
      long long int j = 1;
      while (j < dup) {
        moves.push_back(j);
        moves.push_back(j);
        j += 2;
      }
      moves.push_back(dup - 1);
      moves.push_back(dup - 1);
      dup--;
      j = dup;
      j -= 2;
      while (j >= 2) {
        moves.push_back(j);
        j -= 2;
      }
    } else {
      long long int j = 2;
      while (j < dup) {
        moves.push_back(j);
        moves.push_back(j);
        j += 2;
      }
      dup--;
      moves.push_back(dup);
      moves.push_back(dup);
      j = dup;
      j -= 2;
      while (j >= 1) {
        moves.push_back(j);
        j -= 2;
      }
    }
    cout << moves.size() << endl;
    for (long long int i = 0; i < moves.size(); i++) {
      cout << moves[i] << " ";
    }
    cout << "\n";
    continue;
  }
}