You are given sequences of positive integers $A = (A_1, A_2, \dots, A_X)$, $B = (B_1, B_2, \dots, B_Y)$, and $C = (C_1, C_2, \dots, C_Z)$ of lengths $X$, $Y$, and $Z$, respectively. Here, $X \le Y \le Z$ holds.

You want to rearrange the elements of $C$ such that the resulting sequence contains both $A$ and $B$ as contiguous subsequences.

Determine whether it is possible to achieve this goal. If it is possible, find the lexicographically smallest sequence $C$ after the rearrangement.

You are given $T$ test cases. Solve each of them.

Input

The input is given from Standard Input in the following format:

$$\begin{aligned} &T \\ &\text{case}_1 \\ &\text{case}_2 \\ &\vdots \\ &\text{case}_T \end{aligned}$$

Each case is given in the following format:

$$\begin{aligned} &X \ Y \ Z \\ &A_1 \ A_2 \ \dots \ A_X \\ &B_1 \ B_2 \ \dots \ B_Y \\ &C_1 \ C_2 \ \dots \ C_Z \end{aligned}$$

• All input values are integers.
• $1 \le T \le 10^5$
• $1 \le X \le Y \le Z \le 2 \times 10^5$
• $1 \le A_i \le Z$
• $1 \le B_i \le Z$
• $1 \le C_i \le Z$
• The sum of $X + Y + Z$ over all test cases in a single input is at most $4 \times 10^5$.

Output

Print $T$ lines. The $i$-th line should contain -1 if the goal cannot be achieved for the $i$-th test case, or the lexicographically smallest rearranged $C$ if it can be achieved.

Examples

Input 1

3
2 2 4
4 3
2 1
4 3 2 1
2 3 4
4 3
3 2 1
4 3 2 1
3 3 3
1 1 1
2 2 2
3 3 3

Output 1

2 1 4 3
4 3 2 1
-1

Note

• In the first example, the possible rearranged sequences for $C$ are $(2, 1, 4, 3)$ and $(4, 3, 2, 1)$. Print $(2, 1, 4, 3)$, which is the lexicographically smallest.
• In the second example, the only possible rearranged sequence for $C$ is $(4, 3, 2, 1)$. Print $(4, 3, 2, 1)$.
• In the third example, the goal cannot be achieved. Print -1.