AT_abc460_g [ABC460G] Vertex Flip Query

There is a tree with $ N $ vertices numbered $ 1 $ to $ N $ . The $ i $ -th edge connects vertices $ a_i $ and $ b_i $ . Each vertex $ i $ has a weight $ W_i $ and a color $ C_i \in \lbrace 0,1 \rbrace $ . Process $ Q $ queries. There are three types of queries as follows. - `1 v`: Change $ C_v $ to $ 1 - C_v $ for vertex $ v $ . - `2 v x`: Change $ W_v $ to $ W_v + x $ for vertex $ v $ . - `3 v`: Let $ c $ be the color of vertex $ v $ . Output the sum of weights of all vertices reachable from vertex $ v $ by traveling only through vertices of color $ c $ (including vertex $ v $ itself).

The input is given from Standard Input in the following format, where $ \mathrm{query}_i $ denotes the $ i $ -th query: > $ N $ $ Q $ $ W_1 $ $ W_2 $ $ \dots $ $ W_N $ $ C_1 $ $ C_2 $ $ \dots $ $ C_N $ $ a_1 $ $ b_1 $ $ a_2 $ $ b_2 $ $ \vdots $ $ a_{N-1} $ $ b_{N-1} $ $ \mathrm{query}_1 $ $ \mathrm{query}_2 $ $ \vdots $ $ \mathrm{query}_Q $ Each query is given in one of the following formats: > $ 1 $ $ v $ > $ 2 $ $ v $ $ x $ > $ 3 $ $ v $

Let $ m $ be the number of type- $ 3 $ queries given. Output $ m $ lines. The $ i $ -th line should contain the answer for the $ i $ -th type- $ 3 $ query.

### Sample Explanation 1 For example, for the first query, the set of vertices reachable from vertex $ 1 $ by traveling only through vertices of color $ 0 $ is $ \lbrace 1,2,3,4,5 \rbrace $ . ### Constraints - $ 1 \leq N \leq 3 \times 10^5 $ - $ 1 \leq Q \leq 2 \times 10^5 $ - $ 1 \leq W_i \leq 10^9 $ - $ C_i \in \lbrace 0,1 \rbrace $ - $ 1 \leq a_i \lt b_i \leq N $ - The input graph is a tree. - $ 1 \leq v \leq N $ - $ 1 \leq x \leq 10^9 $ - All input values are integers.