Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/4
K:D
['DF FA Af Ad', 'd A B>B Bd A>B A/G/F/G/ AF', 'd A B>c d>c d2- d B']  
X:1
L:1/8
M:2/4
K:D
 F/E/ | DF FA | Af !>!f/e/d/B/ | Ad dF | E2- E (F/E/) | DF FA | Af !>!f/e/d/B/ | Ad e>d | d2- d || 
 A | B>B Bd | A>B A/G/F/G/ | AF dF | E2- E F/E/ | DF FA | Af !>!f/e/d/B/ | Ad e>d | d2- d |: 
!ff! A | B>c d>c | d2- d B | A>B A>F | A2- A A | !>!DF/F/ !>!FA/A/ | !>!A!>!f !>!f/e/d/B/ | 
 Ad !>!e>d | d2- d :|  