You are given a permutation $a$ of length $n$$^{\text{∗}}$.

We say that a permutation $b$ of length $n$ is good if the two permutations $a$ and $b$ can become the same after performing the following operation at most $n$ times (possibly zero):

• Choose two integers $l, r$ such that $1 \le l \lt r \le n$ and $a_r = \min(a_l, a_{l + 1}, \ldots, a_r)$.
• Cyclically shift the subsegment $[a_l, a_{l + 1}, \ldots, a_r]$ one position to the right. In other words, replace $a$ with $[a_1, \ldots, a_{l - 1}, \; a_r, a_l, a_{l + 1}, \ldots, a_{r - 1}, \; a_{r + 1}, \ldots, a_n]$.

You are also given a permutation $c$ of length $n$ where some elements are missing and represented by $0$.

You need to find a good permutation $b_1, b_2, \ldots, b_n$ such that $b$ can be formed by filling in the missing elements of $c$ (i.e., for all $1 \le i \le n$, if $c_i \ne 0$, then $b_i = c_i$). If it is impossible, output $-1$.

$^{\text{∗}}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2 \le n \le 5 \cdot 10^5$).

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$). It is guaranteed that $a$ is a permutation of length $n$.

The third line of each test case contains $n$ integers $c_1, c_2, \ldots, c_n$ ($0 \le c_i \le n$). It is guaranteed that the elements of $c$ that are not $0$ are distinct.

It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^5$.

Output

For each test case:

• If it is impossible to find such a good permutation $b$, output a single integer $-1$.
• Otherwise, output $n$ integers $b_1, b_2, \ldots, b_n$ — the good permutation $b$ you've found. You need to ensure that for all $1 \le i \le n$, if $c_i \ne 0$, then $b_i = c_i$. If there are multiple answers, output any of them.

Note

In the first test case, $b = [1, 2]$ is a valid answer since after performing the following operation, $a$ and $b$ will become the same:

• Choose $l = 1, r = 2$ and cyclically shift the subsegment $[a_1, a_2]$ one position to the right. Then $a$ will become $[1, 2]$.

In the second test case, $b = [2, 3, 4, 1]$ is a valid answer since after performing the following operation, $a$ and $b$ will become the same:

• Choose $l = 1, r = 2$ and cyclically shift the subsegment $[a_1, a_2]$ one position to the right. Then $a$ will become $[2, 3, 4, 1]$.

In the third test case, $b = [1, 3, 2, 4, 5]$ is a valid answer since after performing the following operation, $a$ and $b$ will become the same:

• Choose $l = 1, r = 3$ and cyclically shift the subsegment $[a_1, a_2, a_3]$ one position to the right. Then $a$ will become $[1, 3, 2, 5, 4]$.
• Choose $l = 4, r = 5$ and cyclically shift the subsegment $[a_4, a_5]$ one position to the right. Then $a$ will become $[1, 3, 2, 4, 5]$.

In the fourth test case, $b = [3, 2, 1, 5, 4]$ is a valid answer since $a$ and $b$ are already the same.

In the fifth test case, it is impossible to find such a good permutation $b$, so you should output $-1$.

In the sixth test case, $b = [3, 2, 1, 5, 4, 6]$ is a valid answer since after performing the following operation, $a$ and $b$ will become the same:

• Choose $l = 2, r = 4$ and cyclically shift the subsegment $[a_2, a_3, a_4]$ one position to the right. Then $a$ will become $[3, 2, 5, 6, 1, 4]$.
• Choose $l = 3, r = 5$ and cyclically shift the subsegment $[a_3, a_4, a_5]$ one position to the right. Then $a$ will become $[3, 2, 1, 5, 6, 4]$.
• Choose $l = 5, r = 6$ and cyclically shift the subsegment $[a_5, a_6]$ one position to the right. Then $a$ will become $[3, 2, 1, 5, 4, 6]$.