  Let $a, b$ and $n$ be nonnegative integers $(b \geq a, \ b > 0, \ n \geq 1)$,
$\mathcal{G}_n(a,b)$ be a multigraph on $n$ vertices in which any pair of
vertices is connected with at least $a$ and at most $b$ edges and \textbf{v =}
$(v_1, v_2, ..., v_n)$ be a vector containing $n$ nonnegative integers. We give
a necessary and sufficient condition for the existence of such orientation of
the edges of $\mathcal{G}_n(a,b)$, that the resulted out-degree vector equals
to \textbf{v}. We describe a reconstruction algorithm. In worst case checking
of \textbf{v} requires $\Theta(n)$ time and the reconstruction algorithm works
in $O(bn^3)$ time. Theorems of H. G. Landau (1953) and J. W. Moon (1963) on the
score sequences of tournaments are special cases $b = a = 1$ resp. $b = a \geq
1$ of our result.
