Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/2=110
M:4/4
K:G
['B2 AG']  
X:1
L:1/8
Q:1/2=110
M:4/4
K:G
"G" D>E DE GA B2 |"C" AG EG"D" BA B<d |"G" D>E DE GA B2 |"C" AG EC"D" D2 D2 ::"G" dd de dc B2 | 
"C" AG EG"D" BA B<d |"G" d>d de dc B2 |"C" AG EC"D" D2 D2 :|  