CF1904D2.Set To Max (Hard Version)

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:

1. choose $l$ and $r$ such that $1 \leq l \leq r \leq n$ .
2. let $x=\max(a_l,a_{l+1},\ldots,a_r)$ .
3. 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).

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.