E. Tree Queriestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a rooted tree consisting of n vertices numbered from 1 to n. The root of the tree is a vertex number 1.A tree is a connected undirected graph with n-1 edges.You are given m queries. The i-th query consists of the set of k_i distinct vertices v_i[1], v_i[2], \dots, v_i[k_i]. Your task is to say if there is a path from the root to some vertex u such that each of the given k vertices is either belongs to this path or has the distance 1 to some vertex of this path.InputThe first line of the input contains two integers n and m (2 \le n \le 2 \cdot 10^5, 1 \le m \le 2 \cdot 10^5) — the number of vertices in the tree and the number of queries.Each of the next n-1 lines describes an edge of the tree. Edge i is denoted by two integers u_i and v_i, the labels of vertices it connects (1 \le u_i, v_i \le n, u_i \ne v_i).It is guaranteed that the given edges form a tree.The next m lines describe queries. The i-th line describes the i-th query and starts with the integer k_i (1 \le k_i \le n) — the number of vertices in the current query. Then k_i integers follow: v_i[1], v_i[2], \dots, v_i[k_i] (1 \le v_i[j] \le n), where v_i[j] is the j-th vertex of the i-th query.It is guaranteed that all vertices in a single query are distinct.It is guaranteed that the sum of k_i does not exceed 2 \cdot 10^5 (\sum\limits_{i=1}^{m} k_i \le 2 \cdot 10^5).OutputFor each query, print the answer — "YES", if there is a path from the root to some vertex u such that each of the given k vertices is either belongs to this path or has the distance 1 to some vertex of this path and "NO" otherwise.ExampleInput
10 6
1 2
1 3
1 4
2 5
2 6
3 7
7 8
7 9
9 10
4 3 8 9 10
3 2 4 6
3 2 1 5
3 4 8 2
2 6 10
3 5 4 7
Output
YES
YES
YES
YES
NO
NO
NoteThe picture corresponding to the example:Consider the queries.The first query is [3, 8, 9, 10]. The answer is "YES" as you can choose the path from the root 1 to the vertex u=10. Then vertices [3, 9, 10] belong to the path from 1 to 10 and the vertex 8 has distance 1 to the vertex 7 which also belongs to this path.The second query is [2, 4, 6]. The answer is "YES" as you can choose the path to the vertex u=2. Then the vertex 4 has distance 1 to the vertex 1 which belongs to this path and the vertex 6 has distance 1 to the vertex 2 which belongs to this path.The third query is [2, 1, 5]. The answer is "YES" as you can choose the path to the vertex u=5 and all vertices of the query belong to this path.The fourth query is [4, 8, 2]. The answer is "YES" as you can choose the path to the vertex u=9 so vertices 2 and 4 both have distance 1 to the vertex 1 which belongs to this path and the vertex 8 has distance 1 to the vertex 7 which belongs to this path.The fifth and the sixth queries both have answer "NO" because you cannot choose suitable vertex u.
10 6
1 2
1 3
1 4
2 5
2 6
3 7
7 8
7 9
9 10
4 3 8 9 10
3 2 4 6
3 2 1 5
3 4 8 2
2 6 10
3 5 4 7

YES YES YES YES NO NO 
['dfs and similar', 'graphs', 'trees', '*1900']