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;
const int N = 505;
int a[N];
vector<int> ans;
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    ans.clear();
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    int p = 1;
    while (p <= n - 2) {
      int u = p;
      for (int i = p + 1; i <= n; i++)
        if (a[i] < a[u]) u = i;
      while (u - 2 >= p)
        swap(a[u], a[u - 2]), swap(a[u], a[u - 1]), u -= 2, ans.push_back(u);
      if (u == p + 1)
        swap(a[u - 1], a[u + 1]), swap(a[u - 1], a[u]), u--, ans.push_back(u),
            ans.push_back(u);
      p++;
    }
    p = n;
    while (p >= 3) {
      int u = p;
      for (int i = p - 1; i; i--)
        if (a[i] > a[u]) u = i;
      while (u + 2 <= p)
        swap(a[u], a[u + 2]), swap(a[u], a[u + 1]), u += 2,
            ans.push_back(u - 2), ans.push_back(u - 2);
      if (u == p - 1)
        swap(a[u + 1], a[u - 1]), swap(a[u], a[u + 1]), u++,
            ans.push_back(u - 2);
      p--;
    }
    int f = 0;
    for (int i = 1; i < n; i++)
      if (a[i] > a[i + 1]) f = 1;
    if (f)
      printf("-1\n");
    else {
      printf("%d\n", ans.size());
      for (int i : ans) printf("%d ", i);
      printf("\n");
    }
  }
  return 0;
}