B'You are given a tree with n weighted vertices labeled from 1 to n rooted at vertex 1 . The parent of vertex i is p_i and the weight of vertex i is a_i . For convenience, define p_1=0 . For two vertices x and y of the same depth ^ dagger , define f(x,y) as follows: You will process q queries. In the i -th query, you are given two integers x_i and y_i and you need to calculate f(x_i,y_i) . ^ dagger The depth of vertex v is the number of edges on the unique simple path from the root of the tree to vertex v . The first line contains two integers n and q ( 2 <= n <= 10^5 ; 1 <= q <= 10^5 ). The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= 10^5 ). The third line contains n-1 integers p_2, ldots, p_n ( 1 <= p_i < i ). Each of the next q lines contains two integers x_i and y_i ( 1 <= x_i,y_i <= n ). It is guaranteed that x_i and y_i are of the same depth. Output q lines, the i -th line contains a single integer, the value of f(x_i,y_i) . Consider the first example: In the first query, the answer is a_4 cdot a_5+a_3 cdot a_3+a_2 cdot a_2+a_1 cdot a_1=3+4+25+1=33 . In the second query, the answer is a_6 cdot a_6+a_2 cdot a_2+a_1 cdot a_1=1+25+1=27 . '...