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 = int(input())
    a = list(map(int,input().split()))
    b = sorted(a)
    c=[]
    for i in range(n-2):
        ind=a[i:].index(b[i])+i
        if a[i]==b[i]:
            continue
        while ind!=i:
            if ind-i>=2:
                c.append(ind-1)
                temp1=a[ind-2]
                temp2=a[ind-1]
                a[ind-2]=a[ind]
                a[ind-1]=temp1
                a[ind]=temp2
                ind-=2
            elif ind-i==1:
                c.append(i+1)
                c.append(i+1)
                temp1=a[i]
                temp2=a[ind+1]
                a[i]=a[ind]
                a[i+1]=temp2
                a[i+2]=temp1
                ind-=1
    if a[-2]<=a[-1]:
        print(len(c))
        for i in c:
            print(i,end=' ')
        print()
    else:
        check=False
        if n>3:
            for i in range(n-3,0,-1):
                if a[i]==a[i-1]:
                    check=True
                    ind=i-1
        if not check:
            if n>=3 and a[-3]==a[-1]:
                c.append(n-2)
                print(len(c))
                for i in c:
                    print(i,end=' ')
                print()
            else:
                print("-1")
        else:
            for i in range(ind+1,n-1):
                c.append(i)
                c.append(i)
            print(len(c))
            for i in c:
                print(i,end=' ')
            print()