CF1797D.Li Hua and Tree

普及/提高-

通过率：0%

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题目描述

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.

输入格式

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.

输出格式

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

输入输出样例

输入#1

7 4
1 1 1 1 1 1 1
1 2
1 3
2 4
2 5
3 6
6 7
1 6
2 3
1 6
1 2

输出#1

2
3
3

输入#2

10 14
-160016413 -90133231 -671446275 -314847579 -910548234 121155052 -359359950 83112406 -704889624 145489303
1 6
1 10
10 8
1 4
3 4
2 7
2 5
3 2
9 8
1 4
2 2
2 4
1 4
1 10
2 10
1 9
1 6
2 8
2 10
1 5
1 8
1 1
2 5

输出#2

-2346335269
-314847579
-476287915
-704889624
121155052
-1360041415
228601709
-2861484545

说明/提示

In the first example:

The initial tree is shown in the following picture:

The importance of the subtree of $6$ is $a_6+a_7=2$ .

After rotating the heavy son of $3$ (which is $6$ ) up, the tree is shown in the following picture:

The importance of the subtree of $6$ is $a_6+a_3+a_7=3$ .

The importance of the subtree of $2$ is $a_2+a_4+a_5=3$ .

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