Given a tree with N nodes, a node is called special if it is an end-point of any of the diameters of the tree. For all the nodes of the tree, find if it is special or not. Thus, return a binary array, where the iᵗʰ value of the array will be 1, in case the iᵗʰ node is special. Else, the iᵗʰ value of the array will be 0.

Note: The diameter of a tree is defined as the number of edges in the longest path of the tree.

For example, consider the tree given below:

(illustration of a tree with nodes 1, 2, and 3)

We can see that this tree has only one diameter, which is the unique path between nodes 1 and 3. The length of the diameter is 2. The end-points of the diameter are 1 and 3. Hence, nodes 1 and 3 are considered special, while node 2 is not considered a special node of the tree.

Function Description

Complete the function isSpecial in the editor below.

isSpecial has the following parameters:

• tree_nodes: The number of nodes in the tree.
• tree_from: The nodes from which the edge is incident onto the other node.
• tree_to: The nodes on which the edge is incident.

Return

• int[n]: an integer array of size N, where the iᵗʰ value of the array is 1, in case the iᵗʰ node is special. Else, the iᵗʰ value will be 0.

Constraints

• 1 ≤ tree_nodes ≤ 10⁵
• tree_from ⊆ {1, tree_to ⊆ {1, tree_nodes}
• ≤ tree_from, tree_to ≤ tree_nodes

Sample Input For Custom Testing

7 6
1 2
2 3
3 4
3 5
1 6
1 7

Sample Output

0 0 0 1 1 1 1

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