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 GCC optimize("Ofast,unroll-loops,-ffloat-store")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
using namespace std;
const int maxn = 505;
int n, a[maxn], c[maxn], id[maxn][maxn];
pair<int, int> b[maxn];
vector<int> ans;
void readf() {
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    b[i] = pair<int, int>(a[i], i);
    c[i] = a[i];
  }
  sort(b + 1, b + n + 1);
  for (int i = 1; i <= n; ++i) a[b[i].second] = i;
  int inv = 0;
  for (int i = 1; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j) inv += (a[i] > a[j]);
  if (inv & 1) {
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j)
        if (c[i] == c[j]) {
          swap(a[i], a[j]);
          goto broken;
        }
  broken:;
  }
  for (int i = 1; i <= n; ++i) b[i] = pair<int, int>(a[i], i);
  sort(b + 1, b + n + 1);
  for (int i = 1; i <= 500; ++i)
    for (int j = 1; j <= n; ++j) id[i][j] = 0;
  for (int i = 1; i <= n; ++i) id[b[i].first][b[i].second] = i;
}
void update(int x, int y) {
  if (a[x] == a[y]) return;
  swap(id[a[x]][x], id[a[x]][y]);
  b[id[a[x]][y]] = pair<int, int>(a[x], y);
  swap(id[a[y]][x], id[a[y]][y]);
  b[id[a[y]][x]] = pair<int, int>(a[y], x);
  swap(a[x], a[y]);
}
void gogo(int pos, int id) {
  for (; pos >= id + 2; pos -= 2) {
    ans.emplace_back(pos - 2);
    update(pos - 1, pos);
    update(pos - 2, pos - 1);
  }
  if (pos == id + 1) {
    int cur = pos - 2;
    if (pos != n) cur = pos - 1;
    ans.emplace_back(cur);
    ans.emplace_back(cur);
    update(cur, cur + 1);
    update(cur + 1, cur + 2);
  }
}
void solve() {
  ans.clear();
  for (int i = 1; i <= n; ++i) {
    int pos = b[i].second;
    if (pos <= i) continue;
    gogo(pos, i);
  }
  for (int i = 1; i < n; ++i)
    if (a[i] > a[i + 1]) {
      cout << -1 << '\n';
      return;
    }
  cout << ans.size() << '\n';
  for (auto x : ans) cout << x << ' ';
  cout << '\n';
}
int main() {
  srand(time(NULL));
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  while (cin >> n) {
    readf();
    solve();
  }
}