Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:D
['GBAG GBAG']  
X:1
L:1/8
M:4/4
K:D
"^A" (3ABc |"D" dAFA"G" GBAG |"D" FAFA"G" GBAG |"D" FDFD"A7" GEGE |"D" FDFD"A7" EA(3ABc | 
"D" dAFA"G" GBAG |"D" FAFA"G" GBAG |"D" FAdA"A7" fedc |"D" d2 f2 d2 :|"^B" cd |"A7" ecAc ecge | 
"D" fdAd fdaf |"A" ecAc ecgf |"E7" edcB"A" A2 A2 |"G" BGDG BGdB |"D" AFDF AFdA |"G" BdcB"A7" AGFE | 
"D" D2 F2 D2 :|  