$x,y \in G$, $o(x) = 2, o(y) = 2, o(xy) = k, k\geq 3$. Show that $D_k \cong \langle x,y\rangle$

Question

I know that $D_k = \{1,r, \dots, r^{k-1}, s, sr, \dots, sr^{k-1} \}$ and that I can use $\phi: s^i r^j \mapsto x^i(xy)^j$. I don't know what can be found using this.