In the cube $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$ , $E , F$ are the midpoints of $A B , B C$ respectively, then
A. Plane $B _ { 1 } E F \perp$ plane $B D D _ { 1 }$
B. Plane $B _ { 1 } E F \perp$ plane $A _ { 1 } B D$
C. Plane $B _ { 1 } E F \parallel$ plane $A _ { 1 } A C$
D. Plane $B _ { 1 } E F \parallel$ plane $A _ { 1 } C _ { 1 } D$