Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:G
['B2 AG F>GAB c2 Bc d>e=fe', 'c2 Bc']  
X:1
L:1/8
M:4/4
K:G
 D | G2 A2 B2 AG | F>GAB c2 Bc | d>e=fe dcAG | G3 F D2 (3DEF | G3 A B2 AG | F>GAB c2 Bc | 
 d>e=fe dcA^F | G4 G3 :| B/c/ | d3 e f2 e2 | d2 cB c2 Bc | d2 =fe dcA^F | G3 F D2 (3DEF | 
 G3 A B2 AF | FGAB c2 Bc | d>e=fe dcA^F | G4 G2 :|  