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 PYTHON3):

Solution:
from sys import *

for t in range(int(stdin.readline())):

    n = int(stdin.readline())
    vec = [int(x) for x in stdin.readline().split()]
    ind = [x for x in range(n)]
    ans = []

    def shift(pos):
        ans.append(pos + 1)
        vec[pos], vec[pos + 1], vec[pos + 2] = vec[pos + 2], vec[pos], vec[pos + 1]

    aux = vec.copy()
    aux.sort()

    for i in range(n) :
        if vec[i] != aux[i]:
            j = 0
            for _ in range(i + 1, n):
                if vec[_] == aux[i]:
                    j = _
                    break

            while j - 2 >= i:
                j -= 2
                shift(j)

            if vec[i] == aux[i] :
                continue

            if i >= n - 2 :
                break

            shift(i)
            shift(i)

    if vec[-1] < vec[-2] and vec[-1] == vec[-3] :
        shift(n - 3)

    if vec[-1] < vec[-2]:
        pos = 0

        for i in reversed(range(1, n - 2)):
            if vec[i] == vec[i - 1]:
                pos = i
                break;

        if pos == 0:
            stdout.write(str(-1) + '\n')
            continue

        for i in reversed(range(pos - 1, n - 2)):
            shift(i)

    if vec[-1] < vec[-2]:

        stdout.write(str(-1) + '\n')
        continue

    stdout.write(str(len(ans)) + '\n')

    for i in ans:
        stdout.write(str(i) + ' ')

    stdout.write('\n')