Problem Statement

Implement depth-first search in an undirected graph.

During the traversal, always select the smallest unvisited vertex as the next one.

Input

Your first line will contain ~v~ and ~e~ as space-separated integers. ~v~ represents the number of vertices in the graph, labelled from ~0~ to ~v-1~, and ~e~ represents the number of edges in the graph.

Your next line will contain ~s~, the source vertex to start the DFS from.

Your next ~e~ lines will contain ~2~ space-separated numbers, specifying that there is an edge between the two specified vertices.

Output

The DFS traversal, separated by line breaks.

Constraints

For all test cases:

• ~2 \le v \le 10^3~
• ~0 \le s \le v-1~
• ~1 \le e \le 10^6~

Example 1

Input

7 6
0
0 1
0 2
1 3
1 4
2 5
2 6

Output

0
1
3
4
2
5
6

Python Template

v, e = map(int, input().split())
s = input()
edges = [tuple(map(int, input().split(" "))) for _ in range(e)]

# print(...)

Recursive Limit

Python has this thing called a recursion limit which is pretty bad. If you want to bypass it, put the following magic words at the start of your file...

import sys
sys.setrecursionlimit(1000000)