1483 - Kth Ancestor of a Tree Node.

Hard

You are given a tree with n nodes numbered from 0 to n - 1 in the form of a parent array parent where parent[i] is the parent of <code>i^th</code> node. The root of the tree is node 0. Find the <code>k^th</code> ancestor of a given node.

The <code>k^th</code> ancestor of a tree node is the <code>k^th</code> node in the path from that node to the root node.

Implement the TreeAncestor class:

• TreeAncestor(int n, int[] parent) Initializes the object with the number of nodes in the tree and the parent array.

• int getKthAncestor(int node, int k) return the <code>k^th</code> ancestor of the given node node. If there is no such ancestor, return -1.

Example 1:

Input "TreeAncestor", "getKthAncestor", "getKthAncestor", "getKthAncestor" [[7, -1, 0, 0, 1, 1, 2, 2], 3, 1, 5, 2, 6, 3]

Output: null, 1, 0, -1

Explanation:

TreeAncestor treeAncestor = new TreeAncestor(7, -1, 0, 0, 1, 1, 2, 2);

treeAncestor.getKthAncestor(3, 1); // returns 1 which is the parent of 3

treeAncestor.getKthAncestor(5, 2); // returns 0 which is the grandparent of 5

treeAncestor.getKthAncestor(6, 3); // returns -1 because there is no such ancestor

Constraints:

• <code>1 <= k <= n <= 5 * 10⁴</code>

• parent.length == n

• parent[0] == -1

• 0 <= parent[i] < n for all 0 < i < n

• 0 <= node < n

• There will be at most <code>5 * 10⁴</code> queries.