## Problem BH. Eulerian cycle ≡

 Author: StdAlg Time limit: 1 sec Input file: input.txt Memory limit: 64 Mb Output file: output.txt

### Statement

You are to write a program that receives an undirected connected graph and finds its Eulerian cycle.

### Input file format

Input file contains two integers N, M. Vertices are numbered with integer numbers from 1 to N. M is the number of edges. Each of following M lines contains a pair of vertex numbers, connected by some edge. There is at most one edge connecting two vertices.

### Output file format

Output file must contain a sequence of vertex numbers in order of traversal in an Eiler cycle. If there does not exist any Eiler cycle, output file must contain  − 1.

### Constraints

1 ≤ N, M ≤ 100000

### Sample tests

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

0.106s 0.021s 15