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 random import randint
it = lambda: list(map(int, input().strip().split()))


def solve():
    N = int(input())
    A = it()

    inversion = 0
    duplicate = None
    for i in range(N):
        for j in range(i):
            if A[j] > A[i]:
                inversion += 1
            elif A[j] == A[i]:
                duplicate = A[j]
            
    if inversion % 2:
        if duplicate is None:
            print(-1)
            return

        l = 2
        for i in range(N - 1, -1, -1):
            if A[i] == duplicate:
                l -= 1
                if l == 0:
                    A[i] += 0.1
                    break

    A = [[a, i] for i, a in enumerate(A)]
    B = sorted(A)

    I = []
    for i in range(N):
        if A[i] == B[i]:
            continue
        
        for idx in range(i + 1, N):
            if A[idx] == B[i]:
                break
    
        while idx > i:
            if idx >= i + 2:
                idx -= 2
                I.append(idx + 1)
                A[idx], A[idx + 1], A[idx + 2] = A[idx + 2], A[idx], A[idx + 1]
            else:
                idx -= 1
                I.extend([idx + 1] * 2)
                A[idx], A[idx + 1], A[idx + 2] = A[idx + 1], A[idx + 2], A[idx]

    print(len(I))
    print(' '.join(map(str, I)))        


if __name__ == '__main__':
    T = int(input())
    for _ in range(T):
        solve()