On the annihilators of Ext modules

Let $R$ be a commutative Noetherian ring, and let $M$ and $N$ be two finitely generated $R$-modules such that $N$ is Gorenstein. ##For each integer $t$ we give a bound under inclusion for the annihilator of $Ext^t_R(M, N)$ in terms of minimal primary decomposition of the zero submodule of $M$, which is independent of the choice of minimal primary decomposition. ##Then, by using that bound, we compute the annihilator of $Ext^t_R(M, N)$ for $t= dim_R(N)- dim_R(M otimes_RN)$.