Problem: You are given a connected undirected simple graph, which has N vertices and M edges. The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i connects vertices A_i and B_i. Your task is to find a path that satisfies the following conditions:

* The path traverses two or more vertices.
* The path does not traverse the same vertex more than once.
* A vertex directly connected to at least one of the endpoints of the path, is always contained in the path.



It can be proved that such a path always exists. Also, if there are more than one solution, any of them will be accepted.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i < B_i \leq N
* The given graph is connected and simple (that is, for every pair of vertices, there is at most one edge that directly connects them).

Input

Input is given from Standard Input in the following format:


N M
A_1 B_1
A_2 B_2
:
A_M B_M


Output

Find one path that satisfies the conditions, and print it in the following format. In the first line, print the count of the vertices contained in the path. In the second line, print a space-separated list of the indices of the vertices, in order of appearance in the path.

Examples

Input

5 6
1 3
1 4
2 3
1 5
3 5
2 4


Output

4
2 3 1 4


Input

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


Output

7
1 2 3 4 5 6 7

Solution (in PYTHON3):

Solution:
# -*- coding: utf-8 -*-
temp=input().split()
N=int(temp[0])
M=int(temp[1])
AB=[[int(j)-1 for j in input().split()] for i in range(M)]

chain=[[] for i in range(N)]#  各頂点の連結先
used=[False for i in range(N)]#使ったかどうか
ans=[]#                        答え（連結順にする）

#連結データ作成
for i in range(M):
	chain[AB[i][0]].append(AB[i][1])
	chain[AB[i][1]].append(AB[i][0])

#少なくとも連結のある頂点を探す
#連結のある頂点をstartに格納
#ansとusedに、使った証拠を残す
#startは後で使うので、nextに移す
start=0
while len(chain[start])==0:
	start+=1
ans.append(start)
used[start]=True
next=start


#連結先が無くなるまで連結する
while True:
	#連結先で、使っていない場所を探す
	for point in chain[next]:
		if used[point]==False:
			break
	else:
		break#for文完走なら、もう完結
	#使ってないところをusedとnextとansに代入して進める
	used[point]=True
	next=point
	ans.append(point)
#逆方向に進める
while True:
	for point in chain[start]:
		if used[point]==False:
			break
	else:
		break
	used[point]=True
	start=point
	ans.insert(0,start)
print(len(ans))
ANS=""
for i in ans:
	ANS+=str(i+1)+" "
print(ANS[:-1])