#P1106D. Lunar New Year and a Wander

    ID: 2791 Type: RemoteJudge 3000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>data structuresdfs and similargraphsgreedyshortest paths*1500

Lunar New Year and a Wander

No submission language available for this problem.

Description

Lunar New Year is approaching, and Bob decides to take a wander in a nearby park.

The park can be represented as a connected graph with nn nodes and mm bidirectional edges. Initially Bob is at the node 11 and he records 11 on his notebook. He can wander from one node to another through those bidirectional edges. Whenever he visits a node not recorded on his notebook, he records it. After he visits all nodes at least once, he stops wandering, thus finally a permutation of nodes a1,a2,,ana_1, a_2, \ldots, a_n is recorded.

Wandering is a boring thing, but solving problems is fascinating. Bob wants to know the lexicographically smallest sequence of nodes he can record while wandering. Bob thinks this problem is trivial, and he wants you to solve it.

A sequence xx is lexicographically smaller than a sequence yy if and only if one of the following holds:

  • xx is a prefix of yy, but xyx \ne y (this is impossible in this problem as all considered sequences have the same length);
  • in the first position where xx and yy differ, the sequence xx has a smaller element than the corresponding element in yy.

The first line contains two positive integers nn and mm (1n,m1051 \leq n, m \leq 10^5), denoting the number of nodes and edges, respectively.

The following mm lines describe the bidirectional edges in the graph. The ii-th of these lines contains two integers uiu_i and viv_i (1ui,vin1 \leq u_i, v_i \leq n), representing the nodes the ii-th edge connects.

Note that the graph can have multiple edges connecting the same two nodes and self-loops. It is guaranteed that the graph is connected.

Output a line containing the lexicographically smallest sequence a1,a2,,ana_1, a_2, \ldots, a_n Bob can record.

Input

The first line contains two positive integers nn and mm (1n,m1051 \leq n, m \leq 10^5), denoting the number of nodes and edges, respectively.

The following mm lines describe the bidirectional edges in the graph. The ii-th of these lines contains two integers uiu_i and viv_i (1ui,vin1 \leq u_i, v_i \leq n), representing the nodes the ii-th edge connects.

Note that the graph can have multiple edges connecting the same two nodes and self-loops. It is guaranteed that the graph is connected.

Output

Output a line containing the lexicographically smallest sequence a1,a2,,ana_1, a_2, \ldots, a_n Bob can record.

Samples

Sample Input 1

3 2
1 2
1 3

Sample Output 1

1 2 3

Sample Input 2

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

Sample Output 2

1 4 3 2 5

Sample Input 3

10 10
1 4
6 8
2 5
3 7
9 4
5 6
3 4
8 10
8 9
1 10

Sample Output 3

1 4 3 7 9 8 6 5 2 10

Note

In the first sample, Bob's optimal wandering path could be 12131 \rightarrow 2 \rightarrow 1 \rightarrow 3. Therefore, Bob will obtain the sequence {1,2,3}\{1, 2, 3\}, which is the lexicographically smallest one.

In the second sample, Bob's optimal wandering path could be 143234151 \rightarrow 4 \rightarrow 3 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1 \rightarrow 5. Therefore, Bob will obtain the sequence {1,4,3,2,5}\{1, 4, 3, 2, 5\}, which is the lexicographically smallest one.