## 程序设计在线评测（Online Judge）

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## 题目描述

You are a hunter chasing a monkey in the forest, trying to shoot it down with your all-powerful automatic
machine gun. The monkey is hiding somewhere behind the branches of one of the trees, out of your sight.
You can aim at one of the trees and shoot; your bullets are capable of going through the branches and killing
the monkey instantly if it happens to be in that tree. If it isn't, the monkey takes advantage of the time
it takes you to reload and takes a leap into a neighbouring tree without you noticing. It never stays in the
same place after a shot. You would like to nd out whether there is an strategy that allows you to capture
the monkey for sure, irrespective of its initial location and subsequent jumps. If so, you need to determine
the shortest sequence of shots guaranteeing this.

As an example, consider the situation in which there are only two neighboring trees in the forest (left
hand side of Figure 2). It is then possible to make sure you capture the monkey by shooting twice at the
same tree. Your rst shot succeeds if the monkey happened to be there in the rst place. Otherwise, the
monkey was behind the other tree and it will necessarily have moved when you shoot for the second time.
However, depending on the shape of the forest it may not possible for you to ensure victory. One example
of this is if there are three trees, all connected to one another (right hand side of Figure 2). No matter where
you aim at, there are always two possible locations for the monkey at any given moment. (Note that here
we are concerned with the worst-case scenario where the monkey may consistently guess your next target
tree).

## 输入

The input consists of several test cases, separated by single blank lines. Each test case begins with a line
containing two integers n and m (1 <= n <= 21); n is the number of trees in the forest, and m is the number
of adjacency relations between trees. Each of the following m lines contains two distinct integers between 0
and n

## 输出

Print a line for each test case. The line should contain the single word Impossible if the task is
impossible. Otherwise, it must contain the shortest sequence of shots with the required property, in the
format L: V1V2 : : : VL, where L is the length of the sequence, and V1; V2; : : : ; VL are space-separated integers
containing the identi ers of the trees to shoot at in the right order. If several shortest sequences exist, print
the lexicographically smallest one. (A sequence is smaller than another in lexicographic order if the rst
element on which they di er is smaller in the rst one).

## 样例输入

2 1
0 1

3 3
0 1
1 2
2 0

4 3
0 1
2 3
1 3

0 0

## 样例输出

2: 0 0
Impossible
4: 1 3 3 1

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