B"You are given a rooted tree, consisting of n vertices. The vertices in the tree are numbered from 1 to n , and the root is the vertex 1 . The value a_i is written at the i -th vertex. You can perform the following operation any number of times (possibly zero): choose a vertex v which has at least one child; increase a_v by 1 ; and decrease a_u by 1 for all vertices u that are in the subtree of v (except v itself). However, after each operation, the values on all vertices should be non-negative. Your task is to calculate the maximum possible value written at the root using the aforementioned operation. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The first line of each test case contains a single integer n ( 2 <= n <= 2 cdot 10^5 ) -- the number of vertices in the tree. The second line contains n integers a_1, a_2, ... , a_n ( 0 <= a_i <= 10^9 ) -- the initial values written at vertices. The third line contains n-1 integers p_2, p_3, ... , p_n ( 1 <= p_i <= n ), where p_i is the parent of the i -th vertex in the tree. Vertex 1 is the root. Additional constraint on the input: the sum of n over all test cases doesn't exceed 2 cdot 10^5 . For each test case, print a single integer -- the maximum possible value written at the root using the aforementioned operation. In the first test case, the following sequence of operations is possible: "...