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:
def g(A,i,y,move):
    n = min(i,y-2)
    A[n-1],A[n],A[n+1] = A[n+1],A[n-1],A[n]
    move.append(max(1,n))
    
def f(A,x,y,move):
    i = A.index(x)+1
    while i<y:
        g(A,i,y,move)
        i+=1
    
for tc in range(int(input())):
    n = int(input())
    A = input().split(' ')
    B = []
    S = []
    Amove = []
    Bmove = []
    for i in range(n):
        A[i] = int(A[i])
        B.append(A[i])
        S.append(A[i])
    S.sort()
    dupin = -1
    for i in range(n-1):
        if S[i] == S[i+1]:
            dupin = i
            break
    if dupin == -1:
        for i in range(n-2):
            f(A,S[n-i-1],n-i,Amove)
        if A[0]>A[1]:
            print(-1)
        else:
            print(len(Amove))
            for i in Amove:
                print(i,end = ' ')
            print()
    else:
        for i in range(n-2):
            f(A,S[n-i-1],n-i,Amove)
        if A[0]<=A[1]:
            print(len(Amove))
            for i in Amove:
                print(i,end = ' ')
            print()
            continue
        elif A[0] == A[2]:
            Amove.append(1)
            Amove.append(1)
            print(len(Amove))
            for i in Amove:
                print(i,end = ' ')
            print()
            continue
        else:
            for i in range(n-2):
                f(B,S[n-i-1],n-i,Bmove)
                if n-i-1 == dupin:
                    g(B,n-i-1,n,Bmove)
                    g(B,n-i-2,n,Bmove)
            print(len(Bmove))
            for i in Bmove:
                print(i,end = ' ')
            print()