Two cylindrical rods $A$ and $B$ made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivities of these rods are: $\frac{L_A}{L_B}=\frac{1}{2}, \frac{r_A}{r_B}=2$ and $\frac{K_A}{K_B}=\frac{1}{2}$. The free ends of rods $A$ and $B$ are maintained at $400 \mathrm{~K}, 200 \mathrm{~K}$, respectively. The temperature of rods interface is $\_\_\_\_$ K , when equilibrium is established.