Telecommunication Partners

An international telecommunication company wants to offer its business subscribers a discount on calls made to a fixed set of telephone numbers chosen by the client. From last year's call records, we say that two companies are Business Partners if one of them made or received a call to or from the other during the year.

Given the partnership relation among the companies and an integer $K$, find the size (number of companies) of the largest set $S$ of companies that satisfies both of the following:

• Every company in $S$ has at least $K$ business partners that are also in $S$ (it may also have partners outside $S$).
• $S$ is connected: from any company in $S$ you can reach any other company in $S$ by following business-partner relationships that stay within $S$.

If no such set exists, the answer is $0$.

The input consists of several test cases. The first line of each test case has three integers $N$, $P$, and $K$. $N$ is the total number of companies subscribed to the service ($1 \le N \le 1000$); companies are identified by numbers from $1$ to $N$. $P$ is the number of business-partner pairs, and $K$ is the minimum number of business partners each company must have inside the final set ($1 \le K \le N-1$).

Each of the next $P$ lines contains two integers $X$ and $Y$ ($1 \le X \le N$, $1 \le Y \le N$, $X \ne Y$), meaning that companies $X$ and $Y$ are business partners. The same pair may appear on more than one line, but it still counts as a single partnership.

A line whose first integer $N$ is $0$ marks the end of the input.

For each test case, print a single line containing the size of the largest set $S$ that satisfies the conditions above.