已知四边形 $\mathrm{ABCD}$ 满足 $\overrightarrow{A D}=\frac{1}{4} \overrightarrow{B C}$, 点 $\mathrm{M}$ 满足 $\overrightarrow{D M}=\overrightarrow{M C}$, 若 $\overrightarrow{B M}=x \overrightarrow{A B}+y \overrightarrow{A D}$, 则 $x y=$.
A
3
B
$-\frac{5}{2}$
C
2
D
$-\frac{1}{2}$
E
F