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C. Propagating tree 본문

0x00 개발/Algorithm

C. Propagating tree

영준이 2015.10.15 19:00

time limit per test2 seconds

memory limit per test256 megabytes

inputstandard input

outputstandard output



출처 : 이번 팀원 들이랑 같이 풀 문제 찾고있는 중 발견('http://codeforces.com/problemset/problem/383/C')

Iahub likes trees very much. Recently he discovered an interesting tree named propagating tree. The tree consists of n nodes numbered from 1 to n, each node i having an initial value ai. The root of the tree is node 1.


This tree has a special property: when a value val is added to a value of node i, the value -val is added to values of all the children of node i. Note that when you add value -val to a child of node i, you also add -(-val) to all children of the child of node i and so on. Look an example explanation to understand better how it works.


This tree supports two types of queries:


  • "1 x val" — val is added to the value of node x;
  • "2 x" — print the current value of node x.

In order to help Iahub understand the tree better, you must answer m queries of the preceding type.


Input

The first line contains two integers n and m (1 ≤ n, m ≤ 200000). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1000). Each of the next n–1 lines contains two integers vi and ui (1 ≤ vi, ui ≤ n), meaning that there is an edge between nodes vi and ui.


Each of the next m lines contains a query in the format described above. It is guaranteed that the following constraints hold for all queries: 1 ≤ x ≤ n, 1 ≤ val ≤ 1000.


Sample test(s)

input

1
2
3
4
5
6
7
8
9
10
11
5 5
1 2 1 1 2
1 2
1 3
2 4
2 5
1 2 3
1 1 2
2 1
2 2
2 4
cs

output

1
2
3
3
3
0
cs


Note
The values of the nodes are [1, 2, 1, 1, 2] at the beginning.

Then value 3 is added to node 2. It propagates and value -3 is added to it's sons, node 4 and node 5. Then it cannot propagate any more. So the values of the nodes are [1, 5, 1,  - 2,  - 1].

Then value 2 is added to node 1. It propagates and value -2 is added to it's sons, node 2 and node 3. From node 2 it propagates again, adding value 2 to it's sons, node 4 and node 5. Node 3 has no sons, so it cannot propagate from there. The values of the nodes are [3, 3,  - 1, 0, 1].

You can see all the definitions about the tree at the following link: http://en.wikipedia.org/wiki/Tree_(graph_theory)



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