B"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. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of testcases. The first line of each testcase contains two integers n and m ( 2 <= n <= 10^6 ; n - 1 <= m <= 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 <= v, u <= 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 . 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. Here are the graphs from the first example. The vertices in the lenient vertex covers are marked red. "...