Circular route#455
In one country, there are cities, connected by a network of roads. The network is arranged so that it is possible to get from any city to any other city by traveling along the roads. The president of the country decided to follow in the footsteps of Franklin Delano Roosevelt and employ the unemployed by building roads, but there were not enough construction materials for new roads, so it was decided to dismantle some old roads to improve the remaining ones.
The president wants to remove several roads that form a circular route (a cycle), so that after removal, it is still possible to get from any city to any other by the remaining roads. Find such a circular route, or report that it does not exist.
The first line contains two integers and — the number of cities and roads respectively (1 \le N \le 100\,000, 2N \le M \le 3N). The next lines describe the roads. Each road is given by the numbers of the cities it connects. The cities are numbered from to . There can be multiple roads between two cities; there can also be a road connecting a city to itself.
Output if the required route does not exist. Otherwise, output the numbers of the cities that form the route.
Example 1