A15893. Forever Winter

A snowflake graph is generated from two integers $x$ and $y$ , both greater than $1$ , as follows:

- Start with one central vertex.
- Connect $x$ new vertices to this central vertex.
- Connect $y$ new vertices to each of these $x$ vertices.

For example, below is a snowflake graph for $x=5$ and $y=3$ . The snowflake graph above has a central vertex $15$ , then $x=5$ vertices attached to it ( $3$ , $6$ , $7$ , $8$ , and $20$ ), and then $y=3$ vertices attached to each of those.

Given a snowflake graph, determine the values of $x$ and $y$ .

The first line contains a single integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases.

The first line of each test case contains two integers $n$ and $m$ ( $2 \leq n \leq 200$ ; $1 \leq m \leq \min\left(1000, \frac{n(n-1)}{2}\right)$ ) — the number of vertices and edges in the graph, respectively.

The next $m$ lines each contain two integers each $u$ and $v$ ( $1 \leq u, v \leq n$ , $u \neq v$ ) — the numbers of vertices connected by an edge. The graph does not contain multiple edges and self-loops.

It is guaranteed that this graph is a snowflake graph for some integers $x$ and $y$ both greater than $1$ .

For each test case, on a separate line output the values of $x$ and $y$ , in that order, separated by a space.

The first test case is pictured in the statement. Note that the output 3 5 is incorrect, since $x$ should be output before $y$ .