Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/16
M:2/4
K:Bb
['caf2 fef2 dbg2 g^fg2', 'agfe dcBA GBeg b4 ABdf']  
X:1
L:1/16
M:2/4
K:Bb
"^A""Bb" !>!f2fb !>!f2fb |"F7" a2ac cdef | a2ae g2ge |"Bb" d^cdg f4 | !>!f2fb !>!f2fb | 
"F7" a2ac cdef | a2ae g2gA |"Bb" B2d2 B2 z2 ::[K:F]"^B""F" caf2 fef2 |"Bb" dbg2 g^fg2 | 
"C7" egc2 egB2 |"F" Acfa c'2c'2 | caf2 fef2 |"Bb" dbg2 g^fg2 | ed'c'2 cbe2 | 
"F" f2a2 f2"_>Teil A" z2 ::[K:Eb]"^C""Eb" Bg^fg ag=fe |"Bb7" e2d2 d^cd2 | Baga bagf | 
"Eb" f2e2 ede2 | Bg^fg ag=fe |"Ab" d2c2 cagf |"Eb" egb2"Bb7" dfb2 |"Eb" e2g2 e2 z2 :: 
"^D""Bb7" agfe dcBA |"Eb" GBeg b4 |"Bb7" ABdf b4 |"Eb" GBeg c'2b2 |"Bb7" agfe dcBA |"Eb" GBeg b4 | 
"Bb7" ABdf bagf |"Eb" e2g2 e2 z2 :|  