Inevitability
Vasya lives at the first vertex of a connected undirected graph with n vertices and m edges. Each day, he walks to school, which is located at vertex number n. Vasya aims to take a different route to school every day, but he has noticed that some edges are used on every possible route. Your task is to identify all such edges.
Input
The first line of the input contains two natural numbers n and m — the number of vertices and edges in the graph, respectively (n ≤ 20000, m ≤ 200000).
The following m lines describe the edges, one per line. Each edge i is defined by two natural numbers b_i and e_i — the endpoints of the edge (1 ≤ b_i, e_i ≤ n).
Output
The first line of the output should contain a single natural number b — the count of edges that Vasya must traverse on any path to school. The second line should list these b edge numbers in ascending order. The edges are numbered starting from one, according to their order in the input.