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Tahsin loves graph theory very much. He is especially 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. Initially 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 containers two integers \(n (1 <= n <= 10^5)\) and \(q (1 <= q <= 10^5)\), denoting the number of nodes in the tree and the number of queries respectively.

The next line contains n integers, \(a_1..a_n\), where \(a_i = 1\), if the light in node i is turned on, and \(a_i = 0\), if the light in node i is turned off.

Each of the next n - 1 lines contains two integers u and v (1 <= u, v <= n), denoting there is an edge between u and v.

The next q lines contains a single integer \(q_i (1 <= q_i <= n)\), denoting the node to be toggled.

Output

For each case, after processing all the queries, print n integers, \(b_1..b_n\), denoting the status of the node.

See the sample test case for input output format.

Sample

1
5 5
0 1 1 1 1 
2 1
3 1
4 2
5 4
1
3
4
5
4

Case 1: 1 0 1 0 1

1
5 5
0 1 1 1 1 
2 1
3 1
4 2
5 4
1
3
4
5
4

Case 1: 1 0 1 0 1