F. Lenient Vertex Covertime limit per test5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor 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.ExamplesInput
4
6 5
1 3
2 4
3 4
3 5
4 6
4 6
1 2
2 3
3 4
1 4
1 3
2 4
8 11
1 3
2 4
3 5
4 6
5 7
6 8
1 2
3 4
5 6
7 8
7 2
4 5
1 2
2 3
3 4
1 3
2 4
Output
YES
001100
NO
YES
01100110
YES
0110
Input
1
10 15
9 4
3 4
6 4
1 2
8 2
8 3
7 2
9 5
7 8
5 10
1 4
2 10
5 3
5 7
2 9
Output
YES
0101100100
Input
1
10 19
7 9
5 3
3 4
1 6
9 4
1 4
10 5
7 1
9 2
8 3
7 3
10 9
2 10
9 8
3 2
1 5
10 7
9 5
1 2
Output
YES
1010000011
NoteHere are the graphs from the first example. The vertices in the lenient vertex covers are marked red.   
4
6 5
1 3
2 4
3 4
3 5
4 6
4 6
1 2
2 3
3 4
1 4
1 3
2 4
8 11
1 3
2 4
3 5
4 6
5 7
6 8
1 2
3 4
5 6
7 8
7 2
4 5
1 2
2 3
3 4
1 3
2 4

YES 001100 NO YES 01100110 YES 0110 
['dfs and similar', 'divide and conquer', 'dsu', 'graphs', 'trees', '*2600']