A cycle graph or circular graph is a graph that consists of a single cycle, or in other words, all the vertices are connected in a closed chain.
You are given an undirected graph on N nodes and M edges. You have to determine if it is a cycle graph.
The nodes are 0-indexed. (0, 1, 2, …, N - 1)
Input Format
The first line contains a single integer T, denoting the number of test cases. The second line contains two integers, N and M as described above. M lines follow. Each contains two integers, u and v, denoting that there is an edge from u to v and v to u.
Constraints
1 <= T <= 10 3 <= N <= 103 1 <= M <= 104
Output Format
For each test case, output “YES” if it is a cycle graph and “NO” otherwise.
Sample Input
2
3 3
0 1
1 2
2 0
4 4
0 1
0 2
0 3
1 3
Sample Output
YES
NO
Explanation
The first is a cycle graph. The second isn’t.