Problem Description

A connected, undirected graph of $N$ vertices and $M$ edges is given to CRB.
A pair of vertices ($u$, $v$) ($u$ < $v$) is called critical for edge $e$ if and only if $u$ and $v$ become disconnected by removing $e$.
CRB’s task is to find a critical pair for each of $M$ edges. Help him!

Input

There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:
The first line contains two integers $N$, $M$ denoting the number of vertices and the number of edges.
Each of the next $M$ lines contains a pair of integers $a$ and $b$, denoting an undirected edge between $a$ and $b$.
1 ≤ $T$ ≤ 12
1 ≤ $N$, $M$ ≤ $10^{5}$
1 ≤ $a$, $b$ ≤ $N$
All given graphs are connected.
There are neither multiple edges nor self loops, i.e. the graph is simple.

Output

For each test case, output $M$ lines, $i$-th of them should contain two integers $u$ and $v$, denoting a critical pair ($u$, $v$) for the $i$-th edge in the input.
If no critical pair exists, output "0 0" for that edge.
If multiple critical pairs exist, output the pair with largest $u$. If still ambiguous, output the pair with smallest $v$.

2
3 2
3 1
2 3
3 3
1 2
2 3
3 1

1 2
2 3
0 0
0 0
0 0

Author

KUT（DPRK）