All Tracks Algorithms Graphs Depth First Search Problem

Monk has become a master in graph and trees, so he is ready with a task for you.

Given a Tree $$T$$ consisting of $$N$$ nodes rooted at node $$1$$, each node has a value, where the value of the $$i^{th}$$ node is $$A[i]$$.

In addition to the tree, you have also been given an integer $$K$$. Now, you need to find in this tree, the number of distinct pairs $$(i,j)$$ where node $$i$$ is an ancestor of node $$j$$, and the XOR of the values of all nodes lying on the path from $$i$$ to $$j$$ is equal to $$K$$.

In short, you need to find the number of pairs $$(i,j)$$, where node $$i$$ is an ancestor of $$j$$,
and :$$ \forall x$$ lying on the path from $$i$$ to $$j$$ inclusive, $$\oplus A[x]$$ = $$K$$.

Here, the $$\oplus$$ symbol denotes the logical XOR operation.

Note:
A node $$x$$ is considered an ancestor of another node $$y$$ if $$x$$ is parent of $$y$$ or $$x$$ is an ancestor of parent of $$y$$. For the purposes of this problem, we consider every node to be an ancestor of itself.

Can you do it ?

Input Format :

The first line contains $$2$$ space separated integers $$N$$ and $$K$$. The next line contains $$N$$ space separated integers. where the $$i^{th}$$ integer denotes $$A[i]$$.

The next line contains $$N-1$$ space separated integers, where the $$i^{th}$$ integer denotes the parent of node $$i+1$$.

Output Format :

Print the required answer on a single line.

Constraints :

$$ 1 \le N \le 10^5 $$

$$ 0 \le K, A[i] \le 2^{20} $$

$$ 1 \le parent[i] < i$$, where $$2 \le i \le N$$