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 FGAB c2', 'A2 Bc']  
X:1
L:1/8
M:4/4
K:G
|: D2 | G4 B2 AG | FGAB c2 c2 | B4 cBAG | F3 G ABcA | G2 d2 B2 AG | FGAB c2 dc | B2 cB A3 G | G6 :: 
 Bc | d2 G2 F2 G2 | A4 A2 Bc | d4 cBAG | FGAB cAGF | G3 A B2 c2 | dcBA B2 AG | c3 d e2 d2 | 
 cdcB A2 Bc | B4 cBAG | FGAB c2 dc | B4 A3 G | G6 :|  