Cuber QQ is interested in locating the best k-degree subgraph in the graph G=(V(G),E(G)).

A subgraph S is a k-degree subgraph of G, if (i) each vertex has at least k degree in S, (ii) S is connected; and (iii) S is maximal, i.e., any supergraph of S is not a k-degree except S itself.



Then Cuber QQ defines the score of a subgraph S. Before the definition of the score, he firstly defines

• n(S): the number of vertices in subgraph S, i.e., n(S) = |V (S)|;
• m(S): the number of edges in subgraph S, i.e., m(S) = |E(S)|;
• b(S): the number of boundary edges in subgraph S, ;

Then he defines the score of a subgraph is , where M,N,B are given constants.

The higher the score of the subgraph, the better Cuber QQ thinks it is. You are asked to find the best k-degree subgraph in the graph G. If there are many k-degree subgraph with the same score, you should maximize k.

The first line contains two integers n and m (), where n and m are the number of nodes and the number of edges in the graph, respectively.

The second line contains three integers M,N and B (), where the score of a subgraph is .

Each of the next m lines contains two integers u and v (, ), meaning that there is an edge between vertices u and v.

The given graph is an undirected graph without any loops and multiple edges.

The only line contains two space-separated integers, which are k and score of the best k-degree subgraph. You should make sure that k>0 .

3 3
1 1 2
1 2
2 3
3 1

2 0