You are given a tree consisting of $N$ vertices. What is the minimum number of vertices that should be removed such that all the remaining parts of the initial tree contain less than $K$ vertices?

Input format

• The first line contains one integer $K$.
• The second line contains one integer $N$.
• The third line contains $N-1$ space-separated integers $a_i$ for $2 \le i \le N$ which means that vertices $i$ and $a_i$ are connected by an edge.

Output format

Print one number denoting the answer to the question.

Constraints

$1 \le K,\ N \le 10 000\\ a_i < i$