Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/16
M:2/4
K:D
['', 'F2AF G2B2 A2f2', 'A2G2 G2 (3def']  
X:1
L:1/16
M:2/4
K:D
 AG |: F2AF G2B2 | A2f2 fef2 | A2e2 ede2 | A2d2 dcdA | F2AF G2B2 | A2f2 f2>f2 | g2e2 ecAc |1 
 e2d2 d2AG :|2 e2d2 d2 (3def |:[K:G] g2gf efge | d2B2 BAGB | c2A2 AFDF | A2G2 G2 (3def | 
 g2>f2 efge | d2B2 BAGB | c2A2 AFDF |1 A2G2 G2 (3def :|2 A2G2 G2 ||  