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 = [int(x) for x in input().split()]
adj = [[] for _ in range(n)]
for _ in range(m):
    u, v = [int(x) for x in input().split()]
    adj[u - 1].append(v - 1)
    adj[v - 1].append(u - 1)
mark = [False for _ in range(n)]
c = [0]
mark[0] = True
while True:
    augmented = False
    for v in adj[c[-1]]:
        if not mark[v]:
            c.append(v)
            augmented = mark[v] = True
            break
    if not augmented:
        break
mark = [False for _ in range(n)]
for v in adj[c[-1]]:
    mark[v] = True
start = 0
for i in range(len(c)):
    if mark[c[i]]:
        start = i
        break
print(len(c) - start)
for i in range(start, len(c)):
    print(c[i] + 1, end=' ')
