Nonsense Time

You are given a permutation $p_1, p_2, \ldots, p_n$ of size n. Initially, all elements of p are frozen. Over n stages, the elements become available one by one. On stage i, the element $p_{k_i}$ becomes available.

For each i, find the longest increasing subsequence among the available elements after the first i stages.

The first line of the input contains an integer T (1 ≤ T ≤ 3), the number of test cases.

In each test case, the first line contains one integer n (1 ≤ n ≤ 50 000), the size of the permutation.

In the second line of each test case, there are n distinct integers $p_1, p_2, \ldots, p_n$ (1 ≤ $p_i$ ≤ n), the permutation.

In the third line of each test case, there are n distinct integers $k_1, k_2, \ldots, k_n$ (1 ≤ $k_i$ ≤ n), describing each stage.

It is guaranteed that $p_1, p_2, \ldots, p_n$ and $k_1, k_2, \ldots, k_n$ are generated uniformly at random among all possible permutations of the given size.

For each test case, print a single line containing n integers, where the i-th integer is the length of the longest increasing subsequence among the available elements after the first i stages.