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Tahsin and Tree

Limits: 1s, 256 MB

Tahsin loves graph theory very much. He is specialy fond of trees. For his upcoming birthday his friends decided to gift him a tree, lets call it birthday tree. Birthday tree consists of n node numbered 1 to n, having a light in every node. Initialy some of the light is turned on and some are turned off. Root of the tree is 1.

The tree has a special property, when a node is toggled, all the children of the node is also toggled. So if you toggle the node i, you also toggle the children of i and so on.

In order to help Tahsin understand the tree better, you are going help him process q queries.

Input

Input starts with T ( 1 <= T <= 5 ).

The first line of every test contains two integers n and q. ( 1 <= n < q <= 105 ). The second line contains n integer a1, a2, …, an, where ai is the initial state of the node i. Each of the next n-1 lines contains two integer ui, vi, ( 1 <= ui, vi <= n ), meaning there is an edge between ui and vi.

Each of the next q line contains an integer x ( 1 <= x <= n ), the node to be toggled.

Constraints

n, q ( 1 <= n < q <= 100000 ).

Output

For each case, after processing all the queries, print n integer b1, b2, …, bn, denoting the status of the node.

See the sample test case for input output format.

Samples

InputOutput
1
4 1
0 1 1 0 
1 4
2 1
3 1
1

Case 1: 1 0 0 1

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