Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=180
M:2/2
K:G
['B2 BA B2 ge', 'e2 ef']  
X:1
L:1/8
Q:1/8=180
M:2/2
K:G
 GA | B2 BA B2 ge | d2 ge dBGA | B2 BA B2 ge | dBAB GFED | B2 BA B2 ge | d2 ge dBGA | B2 BA B2 ge | 
 fedf e2 || ef | gfed eBBd | gfed e2 ef | gfed eBBA | Bedf e2 ef | gfed eBBd | gfed e2 ef | 
 gbag fage | d2 ge dBGA |]  