CF243B.Hydra

One day Petya got a birthday present from his mom: a book called "The Legends and Myths of Graph Theory". From this book Petya learned about a hydra graph.

A non-oriented graph is a hydra, if it has a structure, shown on the figure below. Namely, there are two nodes u and v connected by an edge, they are the hydra's chest and stomach, correspondingly. The chest is connected with h nodes, which are the hydra's heads. The stomach is connected with t nodes, which are the hydra's tails. Note that the hydra is a tree, consisting of h + t + 2 nodes.

Also, Petya's got a non-directed graph G, consisting of n nodes and m edges. Petya got this graph as a last year birthday present from his mom. Graph G contains no self-loops or multiple edges.

Now Petya wants to find a hydra in graph G. Or else, to make sure that the graph doesn't have a hydra.

一天，佩佳收到了妈妈送的生日礼物：一本名为《图论的传说与神话》的书。从这本书中，佩佳了解了“九头蛇图”（hydra graph）的概念。

一个无向图若具有如下图所示的结构，则称为九头蛇图。具体而言，存在两个由一条边相连的节点 $u$ 和 $v$，分别称为九头蛇的“胸部”和“腹部”。胸部与 $h$ 个节点相连，这些节点称为九头蛇的“头部”；腹部与 $t$ 个节点相连，这些节点称为九头蛇的“尾部”。注意：该九头蛇图是一棵树，共包含 $h + t + 2$ 个节点。

此外，佩佳还拥有一张无向图 $G$，它包含 $n$ 个节点和 $m$ 条边。这张图是佩佳去年生日时妈妈送给他的礼物。图 $G$ 中不含自环或重边。

现在，佩佳希望在图 $G$ 中找出一个九头蛇图；否则，需确认图 $G$ 中不存在九头蛇图。

The first line contains four integers n, m, h, t (1 ≤ n, m ≤ 105, 1 ≤ h, t ≤ 100) — the number of nodes and edges in graph G, and the number of a hydra's heads and tails.

Next m lines contain the description of the edges of graph G. The i-th of these lines contains two integers a__i and b__i (1 ≤ a__i, b__i ≤ n, a ≠ b) — the numbers of the nodes, connected by the i-th edge.

It is guaranteed that graph G contains no self-loops and multiple edges. Consider the nodes of graph G numbered with integers from 1 to n.

第一行包含四个整数 $n$、$m$、$h$、$t$（$1 ≤ n, m ≤ 10^5$，$1 ≤ h, t ≤ 100$）—— 分别表示图 $G$ 的节点数、边数，以及九头蛇的头数与尾数。

接下来 $m$ 行描述图 $G$ 的边。其中第 $i$ 行包含两个整数 $a_i$ 和 $b_i$（$1 ≤ a_i, b_i ≤ n$，$a_i ≠ b_i$）—— 表示第 $i$ 条边所连接的两个节点的编号。

保证图 $G$ 中不含自环和重边。图 $G$ 的节点编号为 $1$ 到 $n$ 的整数。

If graph G has no hydra, print "NO" (without the quotes).

Otherwise, in the first line print "YES" (without the quotes). In the second line print two integers — the numbers of nodes u and v. In the third line print h numbers — the numbers of the nodes that are the heads. In the fourth line print t numbers — the numbers of the nodes that are the tails. All printed numbers should be distinct.

If there are multiple possible answers, you are allowed to print any of them.

如果图 $G$ 中不存在九头蛇，则输出 "NO"（不带引号）。

否则，第一行输出 "YES"（不带引号）；第二行输出两个整数——节点 $u$ 和 $v$ 的编号；第三行输出 $h$ 个整数——各头部节点的编号；第四行输出 $t$ 个整数——各尾部节点的编号。所有输出的数字必须互不相同。

若存在多个可行解，输出任意一个即可。

The first sample is depicted on the picture below:

第一个样例在下方图片中展示：