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 
#!/usr/bin/python 

n, m, k = map(int, raw_input().split())

graph = [[] for i in range(n+1)]
for i in range(m) : 
    x, y = map(int, raw_input().split())
    graph[x].append(y)
    graph[y].append(x)

startPoint = max(zip(range(1, n+1), [len(graph[i]) for i in range(1, n+1)]), 
                key = lambda pair: pair[1])[0]
length = k + 1

timer = 0
visit = [0 for i in range(n+1)]
finish = [0 for i in range(n+1)]
pre = [0 for i in range(n+1)]
trace = []
result = []

stack = []
stack.append(startPoint)
flag = True
while len(stack) > 0 and flag : 
    cur = stack[-1]
    if finish[cur] > 0 : 
        stack.pop()
    elif visit[cur] > 0 : 
        timer += 1
        finish[cur] = timer
        trace.pop()
    else : 
        timer += 1
        visit[cur] = timer
        trace.append(cur)
        for adj in graph[cur] : 
            if adj == startPoint and len(trace) >= k+1 : 
                result = trace[:]
                flag = False
                break
            elif visit[adj] == 0 : 
                stack.append(adj)

print len(result)
print " ".join(map(str, result))
