B'You are given a rooted tree on n vertices. The vertices are numbered from 1 to n ; the root is the vertex number 1 . Each vertex has two integers associated with it: a_i and b_i . We denote the set of all ancestors of v (including v itself) by R(v) . The awesomeness of a vertex v is defined as <= ft| sum_{w in R(v)} a_w right| cdot <= ft| sum_{w in R(v)} b_w right|, where |x| denotes the absolute value of x . Process q queries of one of the following forms: The first line contains two integers n and q ( 1 <= q n <= q 2 cdot 10^5, 1 <= q q <= q 10^5 ) -- the number of vertices in the tree and the number of queries, respectively. The second line contains n - 1 integers p_2, p_3, ... , p_n ( 1 <= q p_i < i ), where p_i means that there is an edge between vertices i and p_i . The third line contains n integers a_1, a_2, ... , a_n ( -5000 <= q a_i <= q 5000 ), the initial values of a_i for each vertex. The fourth line contains n integers b_1, b_2, ... , b_n ( -5000 <= q b_i <= q 5000 ), the values of b_i for each vertex. Each of the next q lines describes a query. It has one of the following forms: For each query of the second type, print a single line with the maximum awesomeness in the respective subtree. The initial awesomeness of the vertices is [100, 91, 57, 64, 57] . The most awesome vertex in the subtree of vertex 1 (the first query) is 1 , and the most awesome vertex in the subtree of vertex 2 (the second query) is 2 . After the first update (the third query), the awesomeness changes to [100, 169, 57, 160, 57] and thus the most awesome vertex in the whole tree (the fourth query) is now 2 . After the second update (the fifth query), the awesomeness becomes [100, 234, 57, 240, 152] , hence the most awesome vertex (the '...