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 maxn = 2e5 + 500;
const int mod = 1e9 + 7;
int T, n;
int a[maxn];
vector<int> ans;
void swift(int x) {
  int tmp = a[x + 2];
  a[x + 2] = a[x + 1];
  a[x + 1] = a[x];
  a[x] = tmp;
}
bool slove() {
  ans.clear();
  for (int i = 1; i <= n - 2; i++) {
    int mn = INT_MAX, id;
    for (int j = i; j <= n; j++) {
      if (a[j] < mn) mn = a[j], id = j;
    }
    while (id - 2 >= i) id -= 2, swift(id), ans.push_back(id);
    if (id - 1 == i) swift(i), swift(i), ans.push_back(i), ans.push_back(i);
  }
  for (int i = n; i >= 3; i--) {
    int mx = -1, id;
    for (int j = i; j >= 1; j--) {
      if (a[j] > mx) mx = a[j], id = j;
    }
    if (id == i - 1) swift(id - 1), ans.push_back(id - 1);
  }
  for (int i = 1; i < n; i++) {
    if (a[i] > a[i + 1]) return false;
  }
  return true;
}
int main() {
  cin >> T;
  while (T--) {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) scanf("%d", a + i);
    if (!slove())
      puts("-1");
    else {
      printf("%d\n", ans.size());
      for (int i = 0; i < ans.size(); i++) printf("%d ", ans[i]);
      puts("");
    }
  }
}