CSES - NOI 2019 - Graph Ordering
• Time limit: 1.00 s
• Memory limit: 512 MB

You are given an undirected connected graph that has n nodes. The nodes are numbered 1,2,\dots,n.

Let us consider an ordering of the nodes. The first node in the ordering is called the source, and the last node is called the sink. In addition, a path is called valid if always when we move from node a to node b, node a is before node b in the ordering.

Your task is to find an ordering such that (1) there is a valid path from the source to every node, and (2) there is a valid path from every node to the sink, or determine that it is not possible to create such an ordering.

# Input

The first line has two integers n and m: the number of nodes and edges.

After this, there are m lines that describe the edges. Each line has two integers a and b: there is an edge between nodes a and b.

It is guaranteed that the graph is connected, contains no self-loops and there is at most one edge between every pair of nodes.

# Output

Print any valid ordering of the nodes. If there are no solutions, print "IMPOSSIBLE".

# Example 1

Input:

5 5
4 2
3 4
2 1
3 1
1 5


Output:

4 2 3 1 5


# Example 2

Input:

4 3
1 2
3 2
4 2


Output:

IMPOSSIBLE


• 2 \le n \le 10^{5}
• The graph is a tree.

• 2 \le n \le 100
• 1 \le m \le 200

• 2 \le n \le 2000
• 1 \le m \le 5000