题目描述

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

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.

输入格式

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.

输出格式

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

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

4 2 3 1 5

4 3
1 2
3 2
4 2

IMPOSSIBLE

提示

Subtask 1 (7 points)

• $2 \leq n \leq 10^5$
• The graph is a tree.

Subtask 2 (29 points)

• $2 \leq n \leq 100$
• $1 \leq m \leq 200$

Subtask 3 (18 points)

• $2 \leq n \leq 2000$
• $1 \leq m \leq 5000$

Subtask 4 (21 points)

• $2 \leq n \leq 10^5$
• $1 \leq m \leq 2 \cdot 10^5$
• It is guaranteed that there exists a valid ordering with node 1 as the source, and node $n$ as the sink.

Subtask 5 (25 points)

• $2 \leq n \leq 10^5$
• $1 \leq m \leq 2 \cdot 10^5$