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:
import sys


def rotate(s,i,ans):
    s[i], s[i+1], s[i+2] = s[i+2], s[i], s[i+1]
    ans.append(str(i+1))
    return s, ans


t = int(input())
while t:
    ans = []
    n = int(input())
    s = list(map(int, sys.stdin.readline().split()))
    ss = s.copy()
    ss.sort()
    l = len(ss)
    if l == 3:
        t -= 1
        i = 0
        while True:
            if s == ss:
                print(len(ans))
                print(' '.join(ans))
                break
            s, ans = rotate(s, i, ans)
            if len(ans) == 3:
                print(-1)
                break
        continue

    j = 0
    c = 0
    while j < l:
        k = ss[j]
        i = j + s[j:].index(k)
        while i - 2 >= j:
            i = i - 2
            s, ans= rotate(s,i, ans)
        if i != j:
            if j+2 == l:
                if s[j] == s[j+1]:
                    break
                elif s[j-1] == s[j+1] and j != 0:
                    ans.append(str(j))
                    break
                else:
                    if l > len(set(ss)):
                        for i in range(-2,-l-1,-1):
                            if s[i] == s[i+1]:
                                break
                        if -i % 2 == 1:
                            k = -3
                            while k >= i:
                                ans.append(str(l + k+1))
                                k -= 2
                            ans.append(str(l + i+1))
                            k = 1
                            while i + k < -2:
                                ans.append(str(l + i + k+1))
                                ans.append(str(l + i + k+1))
                                k += 2
                        else:
                            k = -3
                            while k >= i+1:
                                ans.append(str(l + k+1))
                                k -=2
                            ans.append(str(l + i+1))
                            k = 2
                            while i+k < -2:
                                ans.append(str(l + i+k+1))
                                ans.append(str(l + i+k+1))
                                k += 2
                        break
                    else:
                        c = 1
                        print(-1)
                        break
            s, ans = rotate(s,j,ans)
            s, ans = rotate(s,j,ans)
            i -= 1
        j += 1
    if c == 0:
        print(len(ans))
        print(' '.join(ans))
    t -= 1