Problem D. Breadth First Search

Author:StdAlg   Time limit:1 sec
Input file:input.txt   Memory limit:256 Mb
Output file:output.txt  


You are to write a program that receives an unweighted undirected graph and writes all its vertices in order of increasing distance from given vertex S. Distance between vertices A and B is the length of the shortest path from A to B. If there are several vertices such that their distances to S are equal, they may be printed in arbitrary order.

Input file format

Input file contains three integers N, M and S, where M is the number of edges, S is the starting vertex. Vertices are numbered with integer numbers from 1 to N. Each of next M lines contains a pair of integers — numbers of vertices connected by an edge.

Output file format

Output file must contain sequence of vertex numbers sorted by increasing distance from S. If some vertex is not reachable from S, output a single number 1.


0 ≤ N, M ≤ 100000

Sample tests

No. Input file (input.txt) Output file (output.txt)
3 2 1
1 2
2 3
1 2 3

0.065s 0.015s 15