Given a unweighted, undirected graph of N vertices and M edges, vertices are numbered from 1 to N. Also there are K special vertices. You have to answer Q queries. In each query, you're given a vertex V. You have to print shortest distance of nearest special vertex. If there is no special vertex reachable from V, print -1.
Note : Graph doesn't contain multiple edges or self loops and it may be disconnected.
Constraints :
1 <= N, K, Q <= 1e5
1 <= M <= 2e6
Sample Input:
5 3 3 // N M K
1 2 // edge 1
2 3 // edge 2
1 3 // edge 3
1 3 5 // special vertices
5 // Q
1 // V for 1st query
2 // " " " 2nd " "
3 // " " " 3rd " "
4 // " " " 4th " "
5 // " " " 5th " "

Sample Output:
0
1
0
-1
0

P.S. : This problem was asked in Codechef's CCDSAP advanced contest on 22th Sept.,2019. Now it's over.