Given a list of n natural numbers d

Given a list of n natural numbers d1, d2, . . . , dn, show how to decide in polynomial
time whether there exists an undirected graph G = (V, E) whose node degrees are
precisely the numbers d1, d2, . . . , dn. (That is, if V = {v1, v2, . . . , vn}, then the degree
of vi should be exactly di
.) G should not contain multiple edges between the same pair
of nodes, or loop edges with both endpoints equal to the same node.