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 $$$y=3$$$. $\text{[math]}$

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 $$$y$$$.

Input

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 $$$1$$$.

Output

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

Note

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

Forever Winter

Examples