Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:Bb
['FBd f2 d', 'f2 b Beg', 'f3!D.C.! B,DF FAB FDB, B,2 F FAc']  
X:1
L:1/8
M:6/8
K:Bb
 F | FBd f2 d | e2 c d3 | cBc G2 G | edc BAG | FBd f2 d | c2 c d2 B | cBc G2 E | edc B2 || 
 !fermata!FBd e2 c | d2 B c3 | FBd f2 d | e2 c d3 | Beb f2 b | Beg f2 b | Beg fed | cdB f3!D.C.! || 
 B,DF FAB | FDB, B,2 F | FAc cde | cAF F2 F | EGc DFB | CEG B,DF | Bdf fed | cdB f3!D.C.! ||  