CF1178G.The Awesomest Vertex

普及/提高-

通过率：0%

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题目描述

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

$$\left| \sum_{w \in R(v)} a_w\right| \cdot \left|\sum_{w \in R(v)} b_w\right|, $$ where $|x|$ denotes the absolute value of $x$ . Process $q$ queries of one of the following forms: <ul> <li> 1 v x — increase $a\_v$ by a positive integer $x$ . </li><li> 2 v — report the maximum awesomeness in the subtree of vertex $v$$$.

输入格式

The first line contains two integers $n$ and $q$ ( $1 \leq n \leq 2\cdot 10^5, 1 \leq q \leq 10^5$ ) — the number of vertices in the tree and the number of queries, respectively.

The second line contains $n - 1$ integers $p_2, p_3, \dots, p_n$ ( $1 \leq p_i < i$ ), where $p_i$ means that there is an edge between vertices $i$ and $p_i$ .

The third line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $-5000 \leq a_i \leq 5000$ ), the initial values of $a_i$ for each vertex.

The fourth line contains $n$ integers $b_1, b_2, \dots, b_n$ ( $-5000 \leq b_i \leq 5000$ ), the values of $b_i$ for each vertex.

Each of the next $q$ lines describes a query. It has one of the following forms:

1 v x ( $1 \leq v \leq n$ , $1\leq x \leq 5000$ ).
2 v ( $1 \leq v \leq n$ ).

输出格式

For each query of the second type, print a single line with the maximum awesomeness in the respective subtree.

输入输出样例

输入#1

5 6
1 1 2 2
10 -3 -7 -3 -10
10 3 9 3 6
2 1
2 2
1 2 6
2 1
1 2 5
2 1

输出#1

说明/提示

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 sixth query) is now $4$ .

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