Given an undirected graph, print a path from vertex 0 to every other vertex using the Depth-First Search (DFS) algorithm. When multiple vertices can be visited, the smallest numbered vertex has higher priority.

For each query in q queries:

• If there exists a path from vertex 0 to vertex x, print one such path found by DFS.
• If no path exists, print -1.

Input

• The first line contains two integers n, m and q (n ≤ 10^5, m ≤ 2 × 10^5, q ≤ 10^2), representing the number of vertices, edges and queries.
• Then there are m lines, each containing two integers u and v representing an undirected edge connecting u and v (0 ≤ u, v < n).
• The next q lines each contain an integer x, representing the destination vertex (0 ≤ x < n)

  Output

For each query, print one line. If x is reachable from vertex 0, print the vertices on a path from 0 to x separated by spaces. Otherwise, print -1.

Example Input:

4 4 2
0 3
3 2
1 0
0 1
1
2

Example Output:

0->1
0->1->3->2