Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/2=90
M:2/2
K:D
['A>G F>A d>d d2 f>d', 'd>d d2']  
X:1
L:1/8
Q:1/2=90
M:2/2
K:D
 A>G | F>A d>d d2 f>d | (3(cec) A>A A2"^tr" B2 |"^1" (3Adc (3BAG (3FBA (3GFE | F2 D>D D2 A>G | 
 F>A d>d d2 f>d | ce aa a2 c2 |"^1" (3(dfe) (3dcB"^tr" E2"^tr" B2 | A2 A>A A2 :: c>d | 
 e2 A>e f2 A>f | g>fe>d"^tr" c2 ec | d2 bd c2 a>c | d2 b>d c2 ^a2 | 
"^1" (3bag (3fge"^tr" d2"^tr" c2 | B2 B>B B2 A>F | F>A d>d d2 f>d |"^1" (3cec A>A A2"^tr" B2 | 
"^1" (3Adc (3BAG (3FBA (3GFE | F2 D>D D2 A>G | F>A d>d d2 f>d | 
"^2" (4:3:4(c/d/e/f/) g>g"^tr" g2 e2 |"^1" (3fag (3fed A2"^tr""^qu" e2 | d2 d>d d2 A :|  