LETU 10th Practice

#### Start

2019-11-06 13:25 AKST

## LETU 10th Practice

#### End

2019-11-11 13:25 AKST
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# Problem BWhere's My Internet??

Photo by Jerry John from Flickr

A new town is being built far out in the country, and currently there are $N$ houses. People have already started moving in. However, some of the houses aren’t connected to the internet yet, and naturally residents are outraged.

The houses are numbered $1$ to $N$. House number $1$ has already been connected to the internet via a long network cable to a neighboring town. The plan is to provide internet to other houses by connecting pairs of houses with separate network cables. A house is connected to the internet if it has a network cable to another house that’s already connected to the internet.

Given a list of which pairs of houses are already connected by a network cable, determine which houses are not yet connected to the internet.

## Input

The first line of input contains two integers $1 \leq N,M \leq 200\, 000$, where $N$ is the number of houses and $M$ is the number of network cables already deployed. Then follow $M$ lines, each containing a pair of house numbers $1 \leq a, b \leq N$ meaning that house number $a$ and house number $b$ are already connected by a network cable. Each house pair is listed at most once in the input.

## Output

If all the houses are already connected to the internet, output one line containing the string Connected. Otherwise, output a list of house numbers in increasing order, one per line, representing the houses that are not yet connected to the internet.

Sample Input 1 Sample Output 1
6 4
1 2
2 3
3 4
5 6

5
6

Sample Input 2 Sample Output 2
2 1
2 1

Connected

Sample Input 3 Sample Output 3
4 3
2 3
4 2
3 4

2
3
4