Description: Alice and Bob are going to celebrate Christmas by playing a game with a tree of presents. The tree has $$$n$$$ nodes (numbered $$$1$$$ to $$$n$$$, with some node $$$r$$$ as its root). There are $$$a_i$$$ presents are hanging from the $$$i$$$-th node. Before beginning the game, a special integer $$$k$$$ is chosen. The game proceeds as follows: - Alice begins the game, with moves alternating each turn; - in any move, the current player may choose some node (for example, $$$i$$$) which has depth at least $$$k$$$. Then, the player picks some positive number of presents hanging from that node, let's call it $$$m$$$ $$$(1 \le m \le a_i)$$$; - the player then places these $$$m$$$ presents on the $$$k$$$-th ancestor (let's call it $$$j$$$) of the $$$i$$$-th node (the $$$k$$$-th ancestor of vertex $$$i$$$ is a vertex $$$j$$$ such that $$$i$$$ is a descendant of $$$j$$$, and the difference between the depth of $$$j$$$ and the depth of $$$i$$$ is exactly $$$k$$$). Now, the number of presents of the $$$i$$$-th node $$$(a_i)$$$ is decreased by $$$m$$$, and, correspondingly, $$$a_j$$$ is increased by $$$m$$$; - Alice and Bob both play optimally. The player unable to make a move loses the game. For each possible root of the tree, find who among Alice or Bob wins the game. Note: The depth of a node $$$i$$$ in a tree with root $$$r$$$ is defined as the number of edges on the simple path from node $$$r$$$ to node $$$i$$$. The depth of root $$$r$$$ itself is zero. Input Format: The first line contains two space-separated integers $$$n$$$ and $$$k$$$ $$$(3 \le n \le 10^5, 1 \le k \le 20)$$$. The next $$$n-1$$$ lines each contain two integers $$$x$$$ and $$$y$$$ $$$(1 \le x, y \le n, x \neq y)$$$, denoting an undirected edge between the two nodes $$$x$$$ and $$$y$$$. These edges form a tree of $$$n$$$ nodes. The next line contains $$$n$$$ space-separated integers denoting the array $$$a$$$ $$$(0 \le a_i \le 10^9)$$$. Output Format: Output $$$n$$$ integers, where the $$$i$$$-th integer is $$$1$$$ if Alice wins the game when the tree is rooted at node $$$i$$$, or $$$0$$$ otherwise. Note: Let us calculate the answer for sample input with root node as 1 and as 2. Root node 1 Alice always wins in this case. One possible gameplay between Alice and Bob is: - Alice moves one present from node 4 to node 3. - Bob moves four presents from node 5 to node 2. - Alice moves four presents from node 2 to node 1. - Bob moves three presents from node 2 to node 1. - Alice moves three presents from node 3 to node 1. - Bob moves three presents from node 4 to node 3. - Alice moves three presents from node 3 to node 1. Bob is now unable to make a move and hence loses. Root node 2 Bob always wins in this case. One such gameplay is: - Alice moves four presents from node 4 to node 3. - Bob moves four presents from node 5 to node 2. - Alice moves six presents from node 3 to node 1. - Bob moves six presents from node 1 to node 2. Alice is now unable to make a move and hence loses.