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 
from collections import defaultdict

class CycleInGraph():
    def __init__(self,n,m,k,edges):
        self.n, self.m, self.k = n, m, k
        self.edges = edges
        self.edge_map = defaultdict(list)
        for x,y in self.edges:
            self.edge_map[x-1].append(y-1)
            self.edge_map[y-1].append(x-1)

    def print_cycle(self):
        check = [0]*(self.n)
        nodes = [0]
        check[0] = 1
        loop_check = True
        while loop_check:
            loop_check = False
            for v in self.edge_map[nodes[-1]]:
                if check[v] == 0:
                    loop_check = True
                    check[v] = 1
                    nodes.append(v)
                    break
        nodes_map = {nodes[i]: i for i in range(len(nodes))}
        min_pos = min([nodes_map[v] for v in self.edge_map[nodes[-1]]])
        print(len(nodes)-min_pos)
        print(*list(map(lambda x: x+1, nodes[min_pos:])))

n,m,k = list(map(int,input().strip(' ').split(' ')))
edges = []
for i in range(m):
    x,y = list(map(int,input().strip(' ').split(' ')))
    edges.append((x,y))

cg = CycleInGraph(n,m,k,edges)
cg.print_cycle()
