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;
inline int qr() {
  int f = 0, fu = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') fu = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    f = (f << 3) + (f << 1) + c - 48;
    c = getchar();
  }
  return f * fu;
}
const int N = 505;
int T, n, m;
vector<int> ans, seq;
map<int, int> a;
int now;
inline void move(int x) {
  int pos;
  now++;
  if (m - now == 1) {
    if (a[1] > a[2]) {
      if (m == 2) {
        puts("-1");
        return;
      }
      if (a[2] == seq[now - 2])
        ans.push_back(now - 1);
      else {
        int j = -1;
        for (register int i = now - 2; i >= 1; --i)
          if (seq[i] == seq[i - 1]) {
            j = i + 2;
            break;
          }
        if (j == -1) {
          puts("-1");
          return;
        }
        if ((now & 1) == (j & 1)) {
          for (int i = now - 2; i >= j; i -= 2) ans.push_back(i);
          for (int i = now - 1; i >= j + 1; i -= 2) ans.push_back(i);
          ans.push_back(j - 2), ans.push_back(j - 2);
          ans.push_back(j - 1), ans.push_back(j - 1);
          for (int i = j + 1; i <= now - 1; i += 2)
            ans.push_back(i), ans.push_back(i);
          for (int i = j; i <= now - 2; i += 2)
            ans.push_back(i), ans.push_back(i);
        } else {
          for (int i = now - 1; i >= j; i -= 2) ans.push_back(i);
          for (int i = now - 1; i >= j; i -= 2) ans.push_back(i);
          ans.push_back(j - 2), ans.push_back(j - 2), ans.push_back(j - 1);
          for (int i = j; i <= now - 1; i += 2)
            ans.push_back(i), ans.push_back(i);
          for (int i = j - 1; i <= now - 2; i += 2)
            ans.push_back(i), ans.push_back(i);
        }
      }
    }
    printf("%d\n", ans.size());
    for (auto it : ans) printf("%d ", it);
    puts("");
    return;
  }
  for (register int i = 1; i <= n; ++i)
    if (a[i] == x) {
      pos = i;
      break;
    }
  n--;
  for (register int i = pos; i <= n; ++i) a[i] = a[i + 1];
  for (int i = now + pos - 3; i >= now; i -= 2) ans.push_back(i);
  if (!(pos & 1)) {
    ans.push_back(now), ans.push_back(now);
    swap(a[1], a[2]);
  }
}
int main() {
  T = qr();
  while (T--) {
    ans.clear(), seq.clear(), now = 0;
    n = qr(), m = n;
    for (register int i = 1; i <= n; ++i) a[i] = qr(), seq.push_back(a[i]);
    if (n <= 1) {
      puts("0\n");
      continue;
    }
    sort(seq.begin(), seq.end());
    for (register int i = 0; i <= m - 2; ++i) move(seq[i]);
  }
  return 0;
}