B'Mr. Chanek has an orchard structured as a rooted ternary tree with N vertices numbered from 1 to N . The root of the tree is vertex 1 . P_i denotes the parent of vertex i , for (2 <= i <= N) . Interestingly, the height of the tree is not greater than 10 . Height of a tree is defined to be the largest distance from the root to a vertex in the tree. There exist a bush on each vertex of the tree. Initially, all bushes have fruits. Fruits will not grow on bushes that currently already have fruits. The bush at vertex i will grow fruits after A_i days since its last harvest. Mr. Chanek will visit his orchard for Q days. In day i , he will harvest all bushes that have fruits on the subtree of vertex X_i . For each day, determine the sum of distances from every harvested bush to X_i , and the number of harvested bush that day. Harvesting a bush means collecting all fruits on the bush. For example, if Mr. Chanek harvests all fruits on subtree of vertex X , and harvested bushes [Y_1, Y_2, ... , Y_M] , the sum of distances is sum_{i = 1}^M text{distance}(X, Y_i) text{distance}(U, V) in a tree is defined to be the number of edges on the simple path from U to V . The first line contains two integers N and Q (1 <= N, Q, <= 5 cdot 10^4) , which denotes the number of vertices and the number of days Mr. Chanek visits the orchard. The second line contains N integers A_i (1 <= A_i <= 5 cdot 10^4) , which denotes the fruits growth speed on the bush at vertex i , for (1 <= i <= N) . The third line contains N-1 integers P_i (1 <= P_i <= N, P_i ne i) , which denotes the parent of vertex i in the tree, for (2 <= i <= N) . It is guaranteed that each vertex can be the parent of at most 3 other vertices. It is also guaranteed that the height of the tree is not greater than 10$$'...