Codeforces Round 225 (Div. 1) |
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Finished |

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data structures

dfs and similar

trees

*2000

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C. Propagating tree

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIahub 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 *a*_{i}. 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 *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 1000). Each of the next *n*–1 lines contains two integers *v*_{i} and *u*_{i} (1 ≤ *v*_{i}, *u*_{i} ≤ *n*), meaning that there is an edge between nodes *v*_{i} and *u*_{i}.

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.

Output

For each query of type two (print the value of node *x*) you must print the answer to the query on a separate line. The queries must be answered in the order given in the input.

Examples

Input

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

Output

3

3

0

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)

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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