Edge Removal to Disconnect Graph

Given a simple undirected connected graph with \(n\) vertices (numbered from 1) and \(m\) edges, you are allowed to remove an arbitrary set of edges so that:

1. The resulting graph is disconnected.
2. The resulting graph does not contain any isolated vertex (i.e. every vertex has degree at least 1).

Construct such an edge removal scheme or report \(-1\) if it is impossible. If there are multiple valid schemes, output any one of them.

Note: You do not need to minimize the number of removed edges.

inputFormat

The first line contains two integers \(n\) and \(m\) (with \(2 \le n \le 10^5\) and \(n-1 \le m \le 10^5\)), denoting the number of vertices and edges respectively.

Each of the following \(m\) lines contains two integers \(u\) and \(v\) (\(1 \le u, v \le n\) and \(u \neq v\)), representing an edge between vertices \(u\) and \(v\). It is guaranteed that the graph is simple and connected.

outputFormat

If a valid edge removal scheme exists, first output an integer \(k\) representing the number of edges to remove, followed by a line with \(k\) space-separated integers denoting the indices of the edges to be removed (edges are numbered in the order of input, starting from 1). If no valid scheme exists, output \(-1\).

sample

4 4
1 2
2 3
3 4
1 4

2
2 4