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:F
['c<F c>A', 'c<f A>f']  
X:1
L:1/8
M:2/2
K:F
 f | c<F c>A c<F c>A | c<F c>A c2 ce | f<a d>f c<fA<f | GGB>c d2 d>f | c<F c>A c<F c>A | 
 c<F c>A c2 ce | f<a d>f c<fA<f | GGB>c d2 d || f | c<f A>f c<F A>f | c<f A>B c2 (cf) | 
 c<f A>f c<f a>g | f<d c>A AGG>f | c<f A>f c<f A>f | c<f A>B c2 (ce) | f<a d>f c<f A>f | 
 GGB>c d2 d ||  