Link

A school website is being reorganized. It has $N$ pages, numbered from $1$ to $N$, and the homepage is page $1$. The content is fine, but the pages are linked poorly: every page contains exactly one link, and that link points to some other (different) page. Because of this, a visitor who starts at the homepage often has to follow many links to reach a given page, and some pages may not be reachable from the homepage at all.

To improve this, new links may be added anywhere: a new link may be placed on any page and may point to any page. For an integer $K$, the website is called $K$-reachable if every page other than the homepage can be reached from the homepage by following at most $K$ links.

Given the website and the integer $K$, compute the minimum number of links that must be added to make the website $K$-reachable.

The first line contains two integers $N$ and $K$ ($2 \le N \le 500\,000$, $1 \le K \le 20\,000$): the number of pages and the maximum number of links a visitor may follow.

Each of the next $N$ lines contains two different integers $A$ and $B$ ($1 \le A, B \le N$), meaning that the single link on page $A$ points to page $B$.

Print a single integer: the minimum number of additional links needed to make the website $K$-reachable.