Certain extensions of completely splittable modules

We obtain a formula for $\operatorname{Ext}^1_{K\Sigma_r}(D^\lambda,D^\mu)$ where $K$ is a field of characteristic grater than 2, $\Sigma_r$ is the symmetric group of degree $r$, $D^\lambda$ and $D^\mu$ are simple $K\Sigma_r$-modules, $D^\lambda$ is a completely splittable module, and $\lambda$ does not strictly dominate $\mu$.