You are given a rooted tree with \(N\) nodes. Each node has a value \(Val[node]\), associated with it and there is a monkey on each one of the nodes.

Every monkey can only climb up the tree as long as the value of the node he encounters is different from all the previous values.

Consider a pair of monkeys on nodes \(U\) and \(V\). We say that such a pair is good if the distance between \(U\) and \(V\) is \(K\) and the monkeys can possibly meet.

You need to find the expected value of the number of good pairs amongst all the monkeys on a random simple path chosen in the tree.

The expected value can be represented in the form \(P/Q\) where \(P\) and \(Q\) are coprime integers. Output \(PQ^{-1} \% 1000000007 \)

Note

Monkeys can only climb up.
Root of the tree is node \(1\).
Distance between a pair of nodes \((U,V)\) is the number of edges on the simple path from \(U\) to \(V\).
The pairs are unordered.

Input Format

The First line contains integers \(N\) and \(K\).
Next line contains \(N-1\) space seperated integers where the \(i^{th}\) one represents the parent of \((i+1)^{th}\) node.
Next line contains \(N\) space seperated integers where \(i^{th}\) of them represents \(Val[i],\) the value of the \(i^{th}\) node.

Output Format

Print a single integer representing the expected value as asked.

Constraints

\(1 \le K\le N\le 10^5 \)
\(1 \le Val[i] \le 10^5\)