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
['GBdB ecdB', 'dedB G2']  
X:1
L:1/8
M:2/4
K:G
 GBdB ecdB | GBdB cAce | GBdB ecdB |1 cedc BGGD :|2 cedc BGGg |: fdec dBGg | fdec d2 (3efg | 
 GgAg Bgcg |1 dedB G2 Gg :|2 dedB G2 GD ||  