Construction of an Irreducible Module as a Direct Summand

Question

Let $L$ be a finite dimensional semisimple Lie algebra. Let $\lambda_1$, .....,$\lambda_l$ be the fundamental dominant weights for the root system $R$ of $L$. Show how to construct an arbitrary irreducible $L$ module of highest weight $\lambda$ denoted by $V(\lambda)$ where $\lambda$ is an integral dominant weight as a direct summand in a suitable tensor product of modules $V(\lambda_1)$,....,$V(\lambda_1)$(repetitions allowed). I have been stuck with this problem for quite some time now.Thanks for any help.