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:G
['', 'G2>G2 (A2B2) c2(3(BcB) A2G2 (B2d2) (e2ce) d4', 'c4 (cedc) B4 (BdcB) A2>c2 (TB2AF)']  
X:1
L:1/16
M:2/4
K:G
 D2"^A" |: G2>G2 (A2B2) | c2(3(BcB) A2G2 | (B2d2) (e2ce) | d4 A4 | d4 (e2f2) | g2(3(fgf) (e2d2) | 
 (AB^cd) (e2ce) |1 d4 z2 (3(B=cB) :|2 d6 d2"^B" |] d6 f2 | (a2fa) g4 |({d} cBcd) (e2ce) | 
 (d2>B2) A2B2 | c4 (cedc) | B4 (BdcB) | A2>c2 (TB2AF) | G6 B2 | c4 (cedc) | B4 (BdcB) | 
 A2>c2 (TB2AF) | G6 |]  