Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=232
M:4/4
K:G
['B2 AG']  
X:1
L:1/8
Q:1/8=232
M:4/4
K:G
|: dB | G3 A B2 AG | A2 e2 e3 g | d3 B dB AG | AB AG E2 DE | G3 A B2 AG | A2 e2 e3 f | 
 ga ba ge dB | d2 g2 g2 gf | e3 d ef ga | b3 a g2 G2 | A3 B AB cd | e2 A2 A2 dc | BA BG ge dB | 
 AB AG E2 GE | D3 d AB cd | B2 AG G2 :|  