You've got a undirected graph G, consisting of n nodes. We will consider the nodes of the graph indexed by integers from 1 to n. We know that each node of graph G is connected by edges with at least k other nodes of this graph. Your task is to find in the given graph a simple cycle of length of at least k + 1.

A simple cycle of length d (d > 1) in graph G is a sequence of distinct graph nodes v1, v2, ..., vd such, that nodes v1 and vd are connected by an edge of the graph, also for any integer i (1 ≤ i < d) nodes vi and vi + 1 are connected by an edge of the graph.

Input

The first line contains three integers n, m, k (3 ≤ n, m ≤ 105; 2 ≤ k ≤ n - 1) — the number of the nodes of the graph, the number of the graph's edges and the lower limit on the degree of the graph node. Next m lines contain pairs of integers. The i-th line contains integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — the indexes of the graph nodes that are connected by the i-th edge. 

It is guaranteed that the given graph doesn't contain any multiple edges or self-loops. It is guaranteed that each node of the graph is connected by the edges with at least k other nodes of the graph.

Output

In the first line print integer r (r ≥ k + 1) — the length of the found cycle. In the next line print r distinct integers v1, v2, ..., vr (1 ≤ vi ≤ n) — the found simple cycle.

It is guaranteed that the answer exists. If there are multiple correct answers, you are allowed to print any of them.

Examples

Input

3 3 2
1 2
2 3
3 1


Output

3
1 2 3 

Input

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


Output

4
3 4 1 2 
#! /Library/Frameworks/Python.framework/Versions/2.6/bin/python

inp = raw_input().split()

n = int(inp[0])
m = int(inp[1])
k = int(inp[2])

adjList = [set() for i in range(n)]

for i in range(m):
	inp = raw_input().split()
	a = int(inp[0]) - 1
	b = int(inp[1]) - 1
	adjList[a].add(b)
	adjList[b].add(a)

path = [0]
visited = set()
desired = set()
loopFound = False;

while (not(loopFound)):
	for neighbour in adjList[path[-1]]:
		if (neighbour in desired):
			startNode = neighbour
			loopFound = True
			break
		elif (not(neighbour in visited)):
			nextNode = neighbour

	if (not(loopFound)):
		visited.add(path[-1])
		path += [nextNode]
		if (len(path) > k):
			desired.add(path[-(k+1)])

for i in range(len(path)):
	if (path[i] == startNode):
		startInd = i
		break

print len(path) - startInd
for i in range(startInd, len(path)):
	print path[i] + 1,