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:
for _ in range(int(input())):
    n,l,out = int(input()),list(map(lambda x: int(x)- 1, input().split())),[];ll = sorted([(l[i], i) for i in range(n)]);swap = (-1,-1);newl = [0]*n    
    for i in range(n - 1):
        if ll[i][0] == ll[i + 1][0]:swap = (ll[i][1],ll[i+1][1])  
    for i in range(n):newl[ll[i][1]] = i
    l,swapN = newl,0;works,done = True,False
    for i in range(n):
        for j in range(i + 1, n):
            if l[i] > l[j]:swapN += 1
    if swapN & 1:l[swap[0]],l[swap[1]] = l[swap[1]],l[swap[0]]
    def shift(i):out.append(i + 1);l[i],l[i+1],l[i+2] = l[i+2],l[i],l[i+1]       
    while not done:
        for i in range(n):
            if l[i] != i:break
        else:done = True
        if done:break
        for find in range(i + 1, n):
            if l[find] == i:break
        while find - i >= 2:find -= 2;shift(find)
        if find - i == 1:
            if find <= n - 2:shift(find - 1);shift(find - 1)
            else:works = False;break
    if works:print(len(out));print(' '.join(map(str,out)))
    else:print(-1)