Given an undirected connected graph with $n$ vertices and $m$ edges, your task is to find a spanning tree of the graph such that for every vertex in the spanning tree its degree is not larger than $\frac{n}{2}$.
Recall that the degree of a vertex is the number of edges it is connected to.
## Input
There are multiple test cases. The first line of the input contains an integer $T$ indicating the number of test cases. For each test case:
The first line contains two integers $n$ and $m$ ($2 \le n \le 10^5$, $n-1 \le m \le 2 \times 10^5$) indicating the number of vertices and edges in the graph.
For the following $m$ lines, the $i$-th line contains two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$) indicating that there is an edge connecting vertex $u_i$ and $v_i$. Please note that there might be self loops or multiple edges.
It's guaranteed that the given graph is connected. It's also guaranteed that the sum of $n$ of all test cases will not exceed $5 \times 10^5$, also the sum of $m$ of all test cases will not exceed $10^6$.
## Output
For each test case, if such spanning tree exists first output ``Yes`` in one line, then for the following $(n-1)$ lines print two integers $p_i$ and $q_i$ on the $i$-th line separated by one space, indicating that there is an edge connecting vertex $p_i$ and $q_i$ in the spanning tree. If no valid spanning tree exists just output ``No`` in one line.
[samples]
## Note
### Note
For the first sample test case, the maximum degree among all vertices in the spanning tree is 3 (both vertex 1 and vertex 4 has a degree of 3). As $3 \le \frac{6}{2}$ this is a valid answer.
For the second sample test case, it's obvious that any spanning tree will have a vertex with degree of 2, as $2 > \frac{3}{2}$ no valid answer exists.