Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/4
K:G
['', 'B2 BA', 'dB AG']  
X:1
L:1/8
M:2/4
K:G
 D B,A, |: G,2 G,>B, | DB, DG |{A} B2 BA | B2 B/c/d | B2 BA | Bd GB | A2 AB | A2 FD | A,2 A,>B, | 
 CD ED | F2 FE | F3 G | Ad fe |1 de cd | B2 BA | BD B,A, :|2 dc AF | G2 GF | G2 gf |: ef/e/ dB | 
 AB GA | Bd ef | g2 fg | eA AB | d>e dB | GB AG | E2 G>A | Bd dB | d e/f/g/ e | dB AG | B2 Bd | 
 g>e dB | AG AB | d>B AB |1 Gg gf :|2 GD B,A, ||  