Chef has a circular sequence $A$ of $N$ non-negative integers $A_1, A_2, \ldots, A_N$ where $A_i$ and $A_{i+1}$ are considered adjacent, and elements $A_1$ and $A_N$ are considered adjacent.
An operation on position $p$ in array $A$ is defined as replacing $A_p$ by the bitwise OR of elements adjacent to $A_p$. Formally, an operation is defined as:
- If $p = 1$, replace $A_1$ with $A_N | A_{2}$
- If $1 < p < N$, replace $A_p$ with $A_{p-1} | A_{p+1}$
- If $p = N$, replace $A_N$ with $A_{N-1} | A_1$
Here, '|' denotes the bitwise OR operation.
Now, Chef must apply operations at each position exactly once, but he may apply the operations in any order.
Being a friend of Chef, you are required to find a sequence of operations, such that after applying all the $N$ operations, the bitwise OR of the resulting array is $K$, or determine that no such sequence of operations exist.

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $K$ denoting the number of elements, and the required bitwise OR after operations.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output:-----
For each test case, if no valid sequence of operations exist, print -1.
Otherwise, print $N$ space-separated integers in which $i$-th integer denote the position chosen in the $i$-th operation. If there are multiple valid sequences of operations, you may print any valid sequence.

-----Constraints-----
- $1 \le T \le 10^5$
- $3 \le N \le 2*10^5$
- $0 \le A_i, K \le 10^9$
- It's guaranteed that the total length of the arrays in one test file doesn't exceed $10^6$

-----Sample Input:-----
5
3 6
2 1 6
3 6
2 1 5
3 7
2 4 6
3 7
1 2 4
3 7
1 2 6

-----Sample Output:-----
2 1 3
-1
-1
-1
2 3 1

-----Explanation:-----
In the first test case, initially, the sequence is {2, 1, 6}.
- Chef applies the operation on the $2^{nd}$ index, so the sequence converts to {2, 6, 6}.
- Next, Chef applies the operation on the $1^{st}$ index, so the sequence converts to {6, 6, 6}.
- Next, Chef applies the operation on the $3^{rd}$ index, and this time sequence does not change.
The final sequence is {6, 6, 6}, and bitwise OR of this sequence is $6$ that is equal to given $K$.

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