Hit the target on the Bloch sphere

Use the $\theta$ and $\phi$ sliders to set the state to $\lvert{+i}\rangle=\tfrac1{\sqrt2}(\lvert0\rangle+i\lvert1\rangle)$. Recall $\lvert\psi\rangle=\cos\tfrac\theta2\lvert0\rangle+e^{i\phi}\sin\tfrac\theta2\lvert1\rangle$ and $\vec r=(\sin\theta\cos\phi,\sin\theta\sin\phi,\cos\theta)$; the target Bloch vector is $(0,1,0)$.

Starting from $\lvert0\rangle$, prepare $\lvert{+i}\rangle$ using only the gates $H=\tfrac1{\sqrt2}\begin{pmatrix}1&1\\1&-1\end{pmatrix}$ and $S=\begin{pmatrix}1&0\\0&i\end{pmatrix}$, at most two gates in total.