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 
n, m, k = map(int, raw_input().strip().split(' '))
edges = [[] for _ in xrange(n)]

for _ in xrange(m):
    a, b = map(int, raw_input().strip().split(' '))
    a -= 1; b -= 1
    edges[a].append(b)
    edges[b].append(a)

for i in xrange(n):
    edges[i] = sorted(edges[i])

els = [len(edge) for edge in edges]
was = [False for _ in xrange(n)]
was[0] = True
stack = [(0, 0)]
nodes = [-1 for _ in xrange(n)]
nodes[0] = 0
indexes = [0 for _ in xrange(n)]
counter = 1

while stack:
    curr_node, curr_index = stack.pop()
    while curr_index == els[curr_node]:
        counter -= 1
        was[curr_node] = False
        curr_node, curr_index = stack.pop()

    neigh = edges[curr_node][curr_index]
    if was[neigh] and counter - indexes[neigh] >= k + 1:
        print counter - indexes[neigh]
        print ' '.join(map(lambda x: str(x + 1), nodes[indexes[neigh]:counter]))
        exit()
    elif not was[neigh]:
        was[neigh] = True
        nodes[counter] = neigh
        indexes[neigh] = counter
        counter += 1
        stack.append((curr_node, curr_index + 1))
        stack.append((neigh, 0))
    else:
        stack.append((curr_node, curr_index + 1))
