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 
import sys
import threading

def put():
    return map(int, sys.stdin.readline().split())

def dfs(i, h):
    vis[i] =h 
    done[i]=1
    element.append(i)
    for j in graph[i]:
        if vis[j]!=0 and h-vis[j]>=k:
                ind = element.index(j)
                ans.extend(element[ind:])
                raise ValueError
        elif done[j]==0:
            dfs(j,h+1)
    vis[i]=0
    element.pop()

def solve():
    try:
        for i in range(1, n+1):
            if done[i]==0:
                dfs(i,1)
    except:
        print(len(ans))
        print(*ans)
           


n,m,k = put()
graph = [[] for _ in range(n+1)]
for i in range(m):
    x,y = put()
    graph[x].append(y)
    graph[y].append(x)
    
done,vis = [0]*(n+1),[0]*(n+1)
element,ans = [],[]


max_recur_size = 10**5*2 + 1000
max_stack_size = max_recur_size*500
sys.setrecursionlimit(max_recur_size)
threading.stack_size(max_stack_size)
thread = threading.Thread(target=solve)
thread.start()
