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,math,itertools
from collections import Counter,deque,defaultdict
from bisect import bisect_left,bisect_right 
from heapq import heappop,heappush,heapify
mod = 10**9+7
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))

for _ in range(inp()):
    n = inp()
    a = inpl()
    b = a[::]; b.sort()
    res = []
    for i in range(n-2):
        now = b[i]
        for j in range(i,n):
            if a[j] == now: break
        while j-i > 1:
            res.append(j-2+1)
            a[j-2],a[j-1],a[j] = a[j],a[j-2],a[j-1]
            j -= 2
        if j-i == 1:
            res.append(i+1); res.append(i+1);
            a[i],a[i+1],a[i+2] = a[i+1],a[i+2],a[i]
    if a[n-2] > a[n-1]:
        if len(set(a)) == n:
            print(-1); continue
        same = -1
        for i in range(n-1):
            if a[i] == a[i+1]: same = i
        if same == -1:
            for i in range(n-2):
                if a[i] == a[-1]: same = i
        for i in range(same,n-2)[::-1]:
            res.append(i+1)
            
    print(len(res))
    print(*res)