You are given an undirected graph G = (V, E) containing N nodes and M edges. The nodes are numbered from 1 to N. A subset C of V is a vertex cover if for every edge (u, v) ∈ E, at least one of u and v belong to C. Note that C = V is always a vertex cover.
Consider a partition of V into two sets A and B. It is said to be a valid partition, if the following two conditions are satisfied: A should be a vertex cover. And for each i such that 1 ≤ i ≤ n/2, nodes 2i and 2i - 1 don't belong to the same set (i.e. one belongs to set A and the other to set B).
Determine if a valid partition exists. If it exists, provide an example of one valid partition.
The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains two space-separated integers N and M denoting the number of nodes and number of edges in the graph respectively.
Each of the following M lines contains two space-se