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:G
['A>cB A>GF G>AB', 'B2 d d2 d e>de d2 c']  
X:1
L:1/8
M:6/8
K:G
|:"^A" D | D>GG G>FG | A>cB A>GF | G>AB d>cB | A>cB A>GF | G>AB E>FG | D>EF G2 ::"^B" z | d3 c3 | 
 B2 d d2 d | e>de d2 c | B2 d d2 d | e>de d2 c | B2 B B>AG | A>cB A>GF | G>AB d>cB | A>cB A>GF | 
 G>AB E>FG | D>EF G2 :|  