Bipartite realization problem

Problem

The bipartite realization problem is a classical decision problem in graph theory, a branch of combinatorics. Given two finite sequences $(a_1,\dots,a_n)$ and $(b_1,\dots,b_m)$ of natural numbers with $m\leq n$, the problem asks whether there is a labeled simple bipartite graph such that $(a_1,\dots,a_n), (b_1,\dots,b_m)$ is the degree sequence of this bipartite graph.