Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:D
['FDFA dfaf gfed dcBA', 'd2 A2 dfdf cece BcdB BAGF GBGB']  
X:1
L:1/8
M:2/2
K:D
 AG | FDFA dfaf | gfed dcBA | GBGB FAFA | EFGA GFED | FDFA dfaf | gfed dcBA | dfaf bgec | 
 d2 f2 d2 :: A2 | dfdf cece | BcdB BAGF | GBGB FAFA | EFGA GFED | FDFA dfaf | gfed dcBA | 
 dfaf bgec | d2 f2 d2 :|  