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 PYTHON):

Solution:
import sys
range = xrange
input = raw_input

def solve(A):
    n = len(A)
    
    rotations = []
    def rotate(i):
        assert(0 <= i < n - 2)
        rotations.append(i)
        A[i + 1], A[i + 2], A[i] = A[i:i + 3] 

    for i in range(n - 2):
        ind = i
        for j in range(i, n):
            if A[ind] > A[j]:
                ind = j
        while ind >= i + 2:
            rotate(ind - 2)
            ind -= 2
        if ind == i + 1:
            rotate(i)
            rotate(i) 
    assert(len(rotations) <= n*n)
    assert A[:-2] == sorted(A[:-2]) and max(A[:-2]) <= min(A[-2:])

    if A[-3] == A[-1] and not A[-3] <= A[-2] <= A[-1]:
        rotate(n - 3)

    if A == sorted(A):
        print len(rotations)
        print ' '.join(str(x + 1) for x in rotations)
        return True
    
    i = n - 2
    while i >= 0 and A[i] != A[i + 1]:
        i -= 1

    if i < 0:
        return False
    
    for j in reversed(range(i + 2, n - 2)):
        rotate(j)
        rotate(j)
    rotate(i + 1)
    rotate(i)
    
    for j in range(i + 2, n - 2):
        rotate(j)
    
    assert(len(rotations) <= n*n)
    assert(A == sorted(A))
    print len(rotations)
    print ' '.join(str(x + 1) for x in rotations)
    return True

t = int(input())
for _ in range(t):
    n = int(input())
    A = [int(x) for x in input().split()]

    if not solve(A):
        print -1