A15667 | Li Hua and Tree

Li Hua has a tree of $n$ vertices and $n-1$ edges. The root of the tree is vertex $1$ . Each vertex $i$ has importance $a_i$ . Denote the size of a subtree as the number of vertices in it, and the importance as the sum of the importance of vertices in it. Denote the heavy son of a non-leaf vertex as the son with the largest subtree size. If multiple of them exist, the heavy son is the one with the minimum index.

Li Hua wants to perform $m$ operations:

- "1 $x$ " ( $1\leq x \leq n$ ) — calculate the importance of the subtree whose root is $x$ .
- "2 $x$ " ( $2\leq x \leq n$ ) — rotate the heavy son of $x$ up. Formally, denote $son_x$ as the heavy son of $x$ , $fa_x$ as the father of $x$ . He wants to remove the edge between $x$ and $fa_x$ and connect an edge between $son_x$ and $fa_x$ . It is guaranteed that $x$ is not root, but not guaranteed that $x$ is not a leaf. If $x$ is a leaf, please ignore the operation.

Suppose you were Li Hua, please solve this problem.

The first line contains 2 integers $n,m$ ( $2\le n\le 10^{5},1\le m\le 10^{5}$ ) — the number of vertices in the tree and the number of operations.

The second line contains $n$ integers $a_{1},a_{2},\ldots ,a_{n}$ ( $-10^{9}\le a_{i}\le 10^{9}$ ) — the importance of each vertex.

Next $n-1$ lines contain the edges of the tree. The $i$ -th line contains two integers $u_i$ and $v_i$ ( $1\le u_i,v_i\le n$ , $u_i\ne v_i$ ) — the corresponding edge. The given edges form a tree.

Next $m$ lines contain operations — one operation per line. The $j$ -th operation contains two integers $t_{j},x_{j}$ ( $t_{j}\in \{1,2\}$ , $1 \leq x_{j} \leq n$ , $x_{j}\neq 1$ if $t_j = 2$ ) — the $j$ -th operation.

For each query "1 $x$ ", output the answer in an independent line.