Set To Max (Hard Version)
Description
This is the hard version of the problem. The only differences between the two versions of this problem are the constraints on $n$ and the time limit. You can make hacks only if all versions of the problem are solved.
You are given two arrays $a$ and $b$ of length $n$.
You can perform the following operation some (possibly zero) times:
- choose $l$ and $r$ such that $1 \leq l \leq r \leq n$.
- let $x=\max(a_l,a_{l+1},\ldots,a_r)$.
- for all $l \leq i \leq r$, set $a_i := x$.
Determine if you can make array $a$ equal to array $b$.
Each test contains multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the arrays.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$) — the elements of array $a$.
The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($1 \le b_i \le n$) — the elements of array $b$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case, output "YES" (without quotes) if you can make $a$ into $b$ using any number of operations, and "NO" (without quotes) otherwise.
You can output "YES" and "NO" in any case (for example, strings "yES", "yes" and "Yes" will be recognized as a positive response).
Input
Each test contains multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the arrays.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$) — the elements of array $a$.
The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($1 \le b_i \le n$) — the elements of array $b$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, output "YES" (without quotes) if you can make $a$ into $b$ using any number of operations, and "NO" (without quotes) otherwise.
You can output "YES" and "NO" in any case (for example, strings "yES", "yes" and "Yes" will be recognized as a positive response).
5
5
1 2 3 2 4
1 3 3 2 4
5
3 4 2 2 4
3 4 3 4 4
5
3 2 1 1 1
3 3 3 2 2
2
1 1
1 2
3
1 1 2
2 1 2
YES
NO
YES
NO
NO
Note
In the first test case, we can achieve array $b$ by applying a single operation: $(l,r)=(2,3)$.
In the second test case, it can be shown we cannot achieve array $b$ in any amount of operations.
In the third test case, we can achieve array $b$ by applying two operations: $(l,r)=(2,5)$. followed by $(l,r)=(1,3)$.
In the fourth and fifth test cases, it can be shown we cannot achieve array $b$ in any amount of operations.