Geometry: Power of a Point & Mass Points · Medium problem

In $\triangle ABC$, point $D$ lies on $\overline{BC}$ with $BD:DC=1:2$, and point $E$ lies on $\overline{AC}$ with $AE:EC=3:1$. Cevians $\overline{AD}$ and $\overline{BE}$ meet at $P$. Find the ratio $AP:PD$.