A8669 | 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.

The first line contains four integers $n$ , $m$ , $h$ , $t$ ( $1<=n,m<=10^{5}$ , $1<=h,t<=100$ ) — 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 $n$ .

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.