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 v 1, v 2, ..., v d such, that nodes v 1 and v d are connected by an edge of the graph, also for any integer i (1 ≤ i d) nodes v i and v i + 1 are connected by an edge of the graph.
输入描述:
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.
输出描述:
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.
示例1
输入
3 3 2<br />1 2<br />2 3<br />3 1<br />4 6 3<br />4 3<br />1 2<br />1 3<br />1 4<br />2 3<br />2 4<br />
输出
3<br />1 2 3 4<br />3 4 1 2
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