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 rs(): return sys.stdin.readline().rstrip()
def ri(): return int(sys.stdin.readline())
def ria(): return list(map(int, sys.stdin.readline().split()))
def ws(s): sys.stdout.write(s + '\n')
def wi(n): sys.stdout.write(str(n) + '\n')
def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n')


def rotate(a, i):
    t = a[i+2]
    a[i + 2] = a[i + 1]
    a[i + 1] = a[i]
    a[i] = t


def solve(n, a):
    sa = sorted(a)
    s = []

    rolled = False
    i = 0
    while i < n:
        for j in range(i, n):
            if a[j] == sa[i]:
                break
        while j - i >= 2:
            j -= 2
            rotate(a, j)
            s.append(j+1)
        if i+1 == j:
            if i+2 < n:
                rotate(a, i)
                rotate(a, i)
                s.append(i+1)
                s.append(i+1)
            else:
                if rolled:
                    wi(-1)
                    return

                found = False
                for k in range(n-2, 0, -1):
                    if len(set(a[k-1:k+2])) == 2:
                        found = True
                        break
                if found:
                    if a[k-1] == a[k]:
                        rotate(a, k - 1)
                        rotate(a, k - 1)
                        s.append(k)
                        s.append(k)
                    else:
                        rotate(a, k - 1)
                        s.append(k)
                    rolled = True
                    i = k-2
                else:
                    wi(-1)
                    return

        i += 1

    if len(s) <= n*n:
        wi(len(s))
        wia(s)
    else:
        wi(-1)


def main():
    for _ in range(ri()):
        n = ri()
        a = ria()
        solve(n, a)


if __name__ == '__main__':
    main()