CSES - NOI 2019 Open - 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.
• $2 \le n \le 100$
• $1 \le m \le 200$
• $2 \le n \le 2000$
• $1 \le m \le 5000$
• $2 \le n \le 10^{5}$
• $1 \le m \le 2 \cdot 10^{5}$
• It is guaranteed that there exists a valid ordering with node 1 as the source, and node $n$ as the sink.
• $2 \le n \le 10^{5}$
• $1 \le m \le 2 \cdot 10^{5}$