1. If the set $M=\left\{x \left\lvert\, \log _{\frac{1}{2}}(x-1)>-1\right.\right\}$, $N=\left\{x \mid 1<2^{x}<4\right\}$, then $M \cap N=(\quad)$.
(A) $\{x \mid 1<x<3\}$
(B) $\{x \mid 1<x<2\}$
(C) $\{x \mid 0<x<3\}$
(D) $\{x \mid 0<x<2\}$