Connected sums with HP^n or CaP^2 and the Yamabe invariant

Let $M$ be a smooth closed $4k$-manifold whose Yamabe invariant $Y(M)$ is nonpositive. We show that $$Y(M\mathrm{♯}l\mathbb{H}{P}^k\mathrm{♯}m\overline{\mathbb{H}{P}^k})=Y(M),$$ where $l,m$ are nonnegative integers, and $\mathbb{H}{P}^k$ is the quaternionic projective space. When $k=4$, we also have $$Y(M\mathrm{♯}lCa{P}^2\mathrm{♯}m\overline{Ca{P}^2})=Y(M),$$ where $Ca{P}^2$ is the Cayley plane.