Description
The second super-fast computer found by Oganesson takes a graph and outputs a series of vertices that describes a Hamiltonian Cycle. Or at least it often does; sometimes it makes a mistake. You must write a program that takes the input graph and a set of output cycles, and then verifies if each one is correct.
Input Format
The first line contains N and M, the number of vertices and the number of edges in the input graph, respectively.
The next M lines each describe an edge, providing the IDs of the two vertices it connects.
The next line provides T, the number of test cycles.
The final T lines each provides a test cycle with N vertex IDs in the proposed order of traversal.
Constraints
5 ≤ N ≤ 1000
5 ≤ M ≤ 50,000
1 ≤ T ≤ 10
0 ≤ vi < N (for all vi, as vertex IDs)
Output Format
T lines, each with the word "YES" or "NO", indicating whether the associated test cycle is valid.
Example 0
Sample Input
5 6
0 2
0 3
1 3
1 4
2 4
3 4
3
1 3 0 2 4
0 1 2 3 4
2 0 3 1 4
Sample Output
YES
NO
YES
