You are given an undirected graph. For each query, determine whether the given vertex is an articulation point in the graph.

An articulation point is a vertex whose removal (along with all incident edges) increases the number of connected components of the graph.

Input

• The first line contains three integers n, m, q - the number of vertices and the number of queries (1 ≤ n ≤ 5x10^4, 1 ≤ m ≤ 2 x 10^5, q ≤ 300).
• The following m lines each contain two integers u, v (1 ≤ u, v ≤ n) representing an undirected edge between vertices u and v.

• The next q lines each contain a single integer x — the vertex to check.

  Output

• Print q lines.

• For each query, output YES if the vertex is an articulation point, otherwise output NO.

  Example

Input

5 5 3
1 2
2 3
2 4
4 5
3 5
2
3
4

Output

YES
NO
NO