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题目描述

In graph theory, a dominant set for an undirected graph $G = (V, E)$ is a subset $D$ of $V$ such that every vertex not in $D$ is adjacent to at least one member of $D$. Finding the minimum dominant set is an NP-hard problem. Your job is to verify, for a given graph, if a subset of vertices is a dominant set.

输入格式

Each input file contains one test case. For each case, the first line contains 2 positive integers: $n$ ($\le 10^4$), the number of vertices; and $m$ ($\le 10^5$), the number of edges. Then $m$ lines follow, each gives indices of the two ends of an edge. The vertices are indexed from 1 to $n$. Then a positive integer $K$ ($\le 10^3$) is given, followed by $K$ lines of vertex sets. Each set is given in the format:

k v[1] v[2] ... v[k]

where k is the number of vertices in the set, and it is followed by k distinct indices of vertices.

输出格式

For each given set, print in a line yes if it is a dominant set, or no if not.

样例

8 9
1 2
2 3
3 4
4 5
5 6
5 7
6 7
6 1
3 6
4
4 1 3 5 8
5 8 7 6 4 2
5 1 2 3 4 5
8 8 7 6 5 4 3 2 1

yes
yes
no
yes

限制

对于所有的测试用例,限制为1700 ms, 256 MB