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:
res, a = [], []


def rot(i: int) -> None:
    global res, a
    res.append(i + 1)
    a[i], a[i+1], a[i+2] = a[i+2], a[i], a[i+1]
    #print(f'Rotation on {i}: {a}')


def solve():
    global res, a
    res.clear()
    input()
    a = [int(i) for i in input().split()]
    s = sorted(a)
    for i in range(len(a) - 2):
        if a[i] == s[i]:
            continue
        j = a.index(s[i], i, len(a))
        while j != i:
            if j - i >= 2:
                j -= 2
                rot(j)
            else:
                rot(i)
                j += 1
    if any(a[i] > a[i + 1] for i in range(len(a) - 1)):

        for i in range(len(a) - 3, -1, -1):
            while a[i + 2] < a[i] or a[i + 2] < a[i + 1]:
                rot(i)

        if all(a[i] != a[i + 1] for i in range(len(a) - 2)):
            print(-1)
            return

    print(len(res))
    print(' '.join(str(i) for i in res))


t = int(input())
while t > 0:
    t -= 1
    solve()