B'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: 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 <= q t <= q 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 <= n <= 2 cdot 10^5 ) -- the length of the arrays. The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= n ) -- the elements of array a . The third line contains n integers b_1, b_2, ldots, b_n ( 1 <= b_i <= 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. '...