Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
Q:1/2=112
M:2/2
K:G
['G A']  
X:1
L:1/4
Q:1/2=112
M:2/2
K:G
|:"^A""G" B2"^/" B/G/- G |"F" A2"^/" A/=F/- F |"Em" G B"^/" A G |"D7" A F"^/" E D | 
"G" B2"^/" B/G/- G |"F" A2"^/" A/=F/- F |"Em" G B"^/" A G |"D7" A2"G" G2 ::"^B""G" d B/c/"^/" d e | 
"G" d B"^/" A G |"D" A D"^/" D F/G/ |"D7" A F"^/" E D |"G" d B/c/"^/" d e |"G" d B"^/" A G | 
"D" A D"^/" D F/G/ |"D7" A2"G" G2 :|  