Problem C
Cat in a tree

CC BY-2.0, Just a kitten in a tree by Zoe Shuttleworth via Flickr

A cat lives in a tree that has $N$ nodes. She will demarcate her territory by “marking” some of the tree nodes. Marked nodes may not be closer to each other than distance $D$, or the smell will be too overwhelming. Find the maximum number of nodes that the cat can mark.

Input

First line has two integers, $N$ and $D$. The $0$-th node is the root node of the tree. Then follows $N-1$ lines, the $i$-th of which contain a single integer $x_i$ with $0\le x_i<i$ (starting with $i=1$). This means that node $x_i$ is connected to node $i$.

We always have $1\le N,D\le 2\cdot {10}^5$.

Output

Output should contain one integer: the maximum number of nodes that can be marked.

4 3
0
0
1

2

3 1000
0
0

1