Compose a musical piece by integrating the alphabetic representation of the specified sequence and the provided motif.
X:1
L:1/8
Q:1/4=120
M:6/8
K:G
['G3 BAG d2 G BAG', 'g3 gdB']  
X:1
L:1/8
Q:1/4=120
M:6/8
K:G
"^Allegro Vivace" G3 BAG | d2 G BAG | A2 B c2 d | ecA A2 B | G3 BAG | d2 G BAG | ABA B2 A | 
 BGE E3 :: g3 gdB | g3 gdB | A2 B c2 d | ecA A3 | g3 gdB | g3{ba} gdB | AGA B2 A | BGE E3 :|  