Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:A
['c |{G} A2 EF/G/ A/G/F/E/ AC D<FE>C', 'a/g/f/e/ ca dbca']  
X:1
L:1/8
M:2/2
K:A
 c |{G} A2 EF/G/ A/G/F/E/ AC | D<FE>C B,/B,/B, B,>d | c/d/e Ac d/e/f/d/ Bd | c<eB>c A/A/A A :| 
 f/g/ | a/g/f/e/ ca dbca | Aaca B/B/B Bf/g/ | a/g/f/e/ ca dbca | Fd/c/ Be/d/ cA Af/g/ | 
 a/g/f/e/ ca dbca | Aaca f/e/d/c/ B/c/d/f/ | e/d/c/B/ AE FADf | e<ca>c A/A/A A ||  