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 $t= dim_r(n)- dim_r(m otimes_rn)$.