In an undirected bipartite graph, there are two disjoint sets, S1 and S2, such that every edge connects a node in S1 to one in S2. This undirected bipartite graph also satisfies further requirement as follows:
1) There are N1 nodes in S1, and N2 nodes in S2.
2) The maximum degree of each node is 1. In another word, each node has at most 1 link.
3) There are K links totally in the bipartite graph. Obviously, K<=min(N1,N2)
[Question] How many such undirected bipartite graphs exist ?