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:Bb
['d>cd>A F>AF>A d>cd>A F2 (de/f/)', 'b>gb>g e2 f>g']  
X:1
L:1/8
M:2/2
K:Bb
 AB/c/ | d>cd>A F>AF>A | d>cd>A F2 (de/f/) | g>fg>e f>ef>d | c2 A2 A2 fe | d>cd>A F>AF>A | 
 d>cd>A F2 (de/f/) | g>eg>e f>ef>d | A2 d2 d2 :: fg | a>fa>f a>fa>f | b>gb>g e2 f>g | 
 a3 f (3bag (3fed | c2 A2 A2 f>g | a3 f a>ga>g | b>gb>g e2 f>g | a>fa>f b>ge>c | A2 d2 d2 :|  