I. Networking Problem
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a professional network modeled as an undirected graph of $$$n$$$ nodes and $$$m$$$ edges, where node $$$1$$$ represents a connected industry professional. Your goal is to establish a direct connection between yourself (node $$$0$$$) and node $$$1$$$ as efficiently as possible.

It is known that node $$$1$$$ spends much time on the 6th floor of GDC.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \leq n \leq 10^9$$$, $$$1 \leq m \leq 10^9$$$) — the number of nodes and edges. The graph is guaranteed to be connected.

Output

Establish a connection between node $$$0$$$ and node $$$1$$$.

Example
Input
6 7
0 2
2 3
3 4
4 5
5 1
2 5
3 1
Output
??