Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/16
M:4/4
K:F
['D2>B,2G,2>G2 EFGA', 'f2>c2 facf AFAc f2>A2']  
X:1
L:1/16
M:4/4
K:F
 C2 | F2>C2A2>F2 D2>B,2G,2>G2 | EFGA Bcde{e} f4- f2Ac | d2>B2 DFBd c2>A2 CFAc | 
{c} B2>D2{A}G2>F2 EF{A}GF EdcE | [A,F]2>C2A2>F2 D2>B,2G,2>G2 | EFGA Bcde f4- f2Ac | 
 (3d2f2e2{a} (3g3fd2 (3c2f2e2{g} (3f3cA2 | (3G2D2F2 (3E2d2c2{A,} [A,F]4 [A,F]2 |] c2 | 
 f2>c2 facf AFAc f2>A2 | BABc dcBA GFED C2>c2 | f2>c2 facf AFAc f2>A2 | Bdgf ecde{e} f4 f2c2 | 
 f2>c2 facf AFAc f2>A2 | BABc dcBA G^FGA Bcde | fefg abc'd' c'afc AFCA, | Acfa gd'c'e' f'4 f2 |]  