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# Consider parallelogram $ABCD$ with points $S$ and $T$ chosen such that $CS:SD = BT:TC = 2,$as in the picture below: [asy] size(200); pair

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Consider parallelogram ABCD with points S and T chosen such that $$CS:SD = BT:TC = 2$$

as in the picture below:

Let $$\overrightarrow{AB} = \mathbf{v}$$ and $$\overrightarrow{AD} = \mathbf{w}$$. Then there exist constants r, s, t, u such that \begin{align*} \overrightarrow{AT} &= r \mathbf{v} + s \mathbf{w},\\ \overrightarrow{BS} &= t \mathbf{v} + u \mathbf{w}. \end{align*}
Enter r, s, t, u in that order below.

Apr 4, 2019