Description:
You are given a simple connected undirected graph, consisting of $$$n$$$ vertices and $$$m$$$ edges. The vertices are numbered from $$$1$$$ to $$$n$$$.
A vertex cover of a graph is a set of vertices such that each edge has at least one of its endpoints in the set.
Let's call a lenient vertex cover such a vertex cover that at most one edge in it has both endpoints in the set.
Find a lenient vertex cover of a graph or report that there is none. If there are multiple answers, then print any of them.
Input Format:
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.
The first line of each testcase contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 10^6$$$; $$$n - 1 \le m \le \min(10^6, \frac{n \cdot (n - 1)}{2})$$$) — the number of vertices and the number of edges of the graph.
Each of the next $$$m$$$ lines contains two integers $$$v$$$ and $$$u$$$ ($$$1 \le v, u \le n$$$; $$$v \neq u$$$) — the descriptions of the edges.
For each testcase, the graph is connected and doesn't have multiple edges. The sum of $$$n$$$ over all testcases doesn't exceed $$$10^6$$$. The sum of $$$m$$$ over all testcases doesn't exceed $$$10^6$$$.
Output Format:
For each testcase, the first line should contain YES if a lenient vertex cover exists, and NO otherwise. If it exists, the second line should contain a binary string $$$s$$$ of length $$$n$$$, where $$$s_i = 1$$$ means that vertex $$$i$$$ is in the vertex cover, and $$$s_i = 0$$$ means that vertex $$$i$$$ isn't.
If there are multiple answers, then print any of them.
Note:
Here are the graphs from the first example. The vertices in the lenient vertex covers are marked red.