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 starts with $T$ ($1 \le T \le 5$).
The first line of every test contains two integers $n$ ($1 \le n \le 10^5$) and $q$ ($1 \le q \le 10^5$). The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$, where $a_i$ is the initial state of the node $i$. Each of the next $n-1$ lines contains two integer $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$), meaning there is an edge between $u_i$ and $v_i$.
Each of the next $q$ line contains an integer $x$ ($1 \le x \le n$), the node to be toggled.
For each case, after processing all the queries, print $n$ integer $b_1$, $b_2$, ..., $b_n$, denoting the status of the node.
See the sample test case for input output format.
Input | Output |
---|---|
1 4 1 0 1 1 0 1 4 2 1 3 1 1 | Case 1: 1 0 0 1 |